In triangle ABC, side AB has a length of 8 cm and side BC has a length of 5 cm. If the triangle has an area of 10 square centimeters, what is the measure of the angle between sides AB and BC?

135°
150°
120°
45°
30°
60°

Thank you!

Answers

Answer 1
Recall the following formula:

Given a triangle with side lengths a, b, and c. Let the measure of the angle between sides of length a and c be B.

Then, the area of the triangle is given by :

                                 [tex]Area= \frac{1}{2}\cdot a\cdot c \cdot \sin B[/tex].

 In our example we have: Area=10 square cm, a=8 cm, c=5 cm, and we want to find the measure of the angle between the 2 sides a and c.

Substituting in the formula we have:

[tex]10= \frac{1}{2}\cdot 8\cdot 5 \cdot \sin B [/tex]

Thus, [tex]10=20 \sin B[/tex], which means [tex]\sin B = \frac{1}{2} [/tex].

[tex] \frac{1}{2} [/tex] is the sine of [tex]30^{\circ}[/tex], but also [tex]150^{\circ}[/tex].


Answer: both 30, and 150 degrees are possible

Related Questions

BEST ANSWER GETS BRAINLIEST A bird park has black and white birds in the ratio of 8 to 2 as shown below: 8 blackbirds and 2 white birds are shown Which is another ratio that can describe the black to white birds?

Answers

Another ratio is 4 black birds to one white bird

4 black birds and 1 white bird

What is the measure of E, in degrees?
A. 130
B. 155
C. Cannot be determined
D. 125


Please don't answer just for points!

Answers

Okay, so with Isosceles triangles, because the two sides are equal, the two angles are as well. This means that angle D and angle F are 25%, so your answer is  180-50=E!

The measure of angle E is 0 degrees not provided in the options (A, B, C, or D), and the correct answer is "Cannot be determined."

To find the measure of angle E in degrees that the sum of angles in a triangle is 180 degrees.

From the given triangle, two angles with measures 50 degrees each (angle A and angle B), and one angle with a measure of 80 degrees (angle D).

To find the measure of angle E, we can use the equation:

Angle E = 180° - (angle A + angle B + angle D)

Angle E = 180° - (50° + 50° + 80°)

Angle E = 180° - 180°

Angle E = 0°

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What is 67.50 with 5 percent sales tax

Answers

3.375 is your answer
70.88 is your total answer

london buys 3 more packs of trading cards today. each pack has 8 cards. write a multiplication sentence to show how many cards landon buys today. then find how many cards landon has now.

Answers

The answer to this question is 24

What is 20 tiles in 5 rows array

Answers

Your question is incomplete.  What were you hoping to compute?

If you start with 20 tiles and arrange them in 5 rows, then you have (20/5), 
or 4, tiles per row.

What is the distance between points 
(9, −7)
and 
(9, 4)
on a coordinate plane?

Answers

The answer would be 11 because the x's 9 doesnt have to move because they're on the same point. If you take 7 away from -7 you get zero. Add 4 to that 7 and you get 11. Make sesnse?
Hope this helped!

Final answer:

The distance between the points (9, -7) and (9, 4) is calculated by finding the absolute difference between the y-coordinates since the x-coordinates are the same. The distance is 11 units.

Explanation:

To calculate the distance between two points on a coordinate plane, you can use the distance formula, which is derived from the Pythagorean theorem. However, in this particular case, since the x-coordinates of the points (9, -7) and (9, 4) are the same, the distance is simply the absolute difference between the y-coordinates.

The formula to find the distance between two points (x1, y1) and (x2, y2) is:

d = √((x2 - x1)² + (y2 - y1)²)

So, substituting the known values:

d = √((9 - 9)² + (4 - (-7))²) = √(0 + 11²) = √121 = 11

Therefore, the distance between the points (9, -7) and (9, 4) on a coordinate plane is 11 units.

HELP ASAP


Angelica swims 14 3/7 hours per month. If she swims the same amount every month, how many hours does she swim in 6 months?

Answers

multiply 14 over 7 to get the number as one fraction. after adding three to that product, you get 101/7. Multiply that by 6/1 to get 606/7, then divide 606 by 7 to get 86 4/7 hours every 6 months.
Just multiply 14 3/7 by 6 to get your answer.

4+5=9 write the doubles fact used to solve

Answers

3X3? Is that what you’re looking for?

Write about a real-world situation that can be solved using a two-step equation. Then write the equation and solve the problem.

Answers

Final answer:

A real-world situation that can be solved using a two-step equation is calculating the total cost of a shopping trip. Let's say you go to a store and buy some items. Each item costs $5, and you buy 3 items. You also have a $10 coupon. To find the total cost, we can use a two-step equation: 3 * 5 - 10 = x. Solving the equation, we get x = 15.

Explanation:

A real-world situation that can be solved using a two-step equation is calculating the total cost of a shopping trip. Let's say you go to a store and buy some items. Each item costs $5, and you buy 3 items. You also have a $10 coupon. To find the total cost, we can use a two-step equation:

Step 1: Write the equation. Let x be the total cost.

Step 2: Solve the equation. The cost of the items is $5 per item, so the first step is to multiply 3 (number of items) by 5 (cost per item). Then subtract the $10 coupon from the total cost. The equation becomes 3 * 5 - 10 = x. Solving the equation, we get x = 5. Therefore, the total cost of the shopping trip is $15.

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A baseball dropped from the roof of a tall building takes 5.23 second s to reach the ground. How tall is the building?

Answers

The most general formula useful here would be

s = s0 + v0*t + (1/2)at^2, where s0 is the original height, v0 is the original velocity, a is the acceleration, and t is the time.

Here, s becomes 0 (baseball is on the ground)
           v0 is 0, since the initial speed of the ball was 0.
            a is the acc'n due to gravity, and is -9.8 m per (sec)^2 in the metric sys.
            t is known and is 5.23 sec

All that is left to find is s0, the original height (which is the building height).

0 = s0 + (0)(5.23 sec) + (1/2) (-9.8 m per sec^2)(5.23 sec)^2

 -s0     =         0             - (4.9 m per sec^2) ( 27.35 sec^2)

 So               s0 = 134 meters (approx)

The building height was approx. 134 meters.


Question:

Find equivalent expressions for the given expressions.

A. 5/6(x - 6) + 1/6(3 - x)

B. (y + 7)4 + 8 - 5y

SHOW WORK  50pts

Answers

5/2 times x is 5/2x and 5/2 times negative 6 is negative 15 so right now u would have 5/2x - 15 + 1/6 (3-x) then distribute 1/6 into 3 and get 5/2x minus 15 plus 0.5 minus 1/6x then combine all like terms so then it would be 2.666666667x minus 15.5 rounded would be 2.7xminus15.5

Answer:

2 x /3 − 9/ 2

− y + 36

What is the area of this polygon 15m 10m 8m 9m

Answers

the area of the polygon is 10,800
Final answer:

The provided data is insufficient to accurately calculate the area of the polygon. With an assumption that the shape is a rectangle and the lengths are 15m and 8m, the area would be 120 square meters.

Explanation:

To calculate the area of a polygon, it's ideal to break down the polygon into simpler shapes like rectangles or triangles, for which we have well established formula for area. However, the information you've provided is inadequate to define a specific polygon shape like a rectangle or a square. Four sides could suggest a rectangle or a quadrilateral, but we don't know two essential properties: the arrangement of these sides and the measure of angles. For instance, if it was a rectangle, we'd look for pairs of equal lengths. If your shape is indeed a rectangle, and we assume that 15m and 8m are the length and width (or vice versa), we could calculate the area. For a rectangle, the area is calculated as length multiplied by width. In this case, it would be 15m*8m = 120 square meters.

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A road has a speed limit of 40 mi/h. Write an inequality that describes the legal speeds r for motor vehicles.


a r < 40

b r <_40

c r _> 40

d r > 40

Answers

This is the answer - B) r <_40
- thanks (: -

Bob can row 14 mph in still water. The total time to travel downstream and return upstream to the starting point is 2.8 hours. If the total distance downstream and back is 36 miles, determine the speed of the river (current speed).

Answers

36/2=18
18/14+c +18/14-c=2.8
18(14-c)+18(14+c)=2.8(196-c²)
504=548.8-2.8c²
2.8c²=44.8
c²=16
c=±4
The current flows at 4 mph
☺☺☺☺

We have that for the Question ,it can be said that The speed pf the river is

3mph

From the question we are told

Bob can row 14 mph in still water. The total time to travel downstream and return upstream to the starting point is 2.8 hours. If the total distance downstream and back is 36 miles, determine the speed of the river (current speed).

Generally the equation for the time  is mathematically given as

[tex]t=\frac{d}{v}\\\\Therefore\\\\3=\frac{12}{9+x}+\frac{12}{9+x}[/tex]

[tex]1/4=\frac{12}{9^2=x^2}\\\\x^2=81-71\\\\\x=\pm 3\\\\x=3[/tex]

Therefore

The speed pf the river is 3mph

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If the Alexanders completed the 735 mi. trip in 15 hr., what was their average rate of travel?

Answers

The average rate of travel was 49 mi /hr. To find the average rate/speed, you just divide the overall distance by the overall time. In this case, 735 mi/ 15 hrs, give you the average rate/speed of 49 mi/hr

Simplify the expression. w - .25w

Answers

Combine like terms.

1w - 0.25w = 0.75w

Hope this helps!

What is 6 1/6 as a Decimal Please!

Answers

6 1/6 as a decimal is 6.16666667
6 1/6 = 6.166666666...well basically six goes on forever.

Hope this helps:)

what is the flope line that is parallel of
[tex]y = 2x + 4[/tex]

Answers

The slope of y = 2x + 4 is 2.
Parallel lines have the same slope, so any line that is parallel to y = 2x + 4 also has slope 2.

2 PART QUESTION

Ted likes to run long distances. He can run 20km in 95 minutes. He wants to know how many kilometers (k) he will go if he runs at the same pace for 285 minutes. What proportion could Ted use to model this situation?

A.) k/20= 95/285
B.) 285/95=k/20

Solve the proportion to determine how far Ted will run in 285 minutes?

Answers

The first answer is B because the bottom half of the proportions are how many km/minutes he CAN run, while the top half of the proportion is how many he WILL run.

He will run 60km in 285 minutes.

A box of cereal contains 23.4 ounces. It costs $5.49. What is the cost to the nearest cent of the cereal per ounce

Answers

So in a proportion 23.4 over 5.49 equals 1 over o and multiply 5.49•1=23.4o
5.49=23.4o divide by 23.4 on both sides and that equals 4.26 per oz

Answer:

The cost of one ounce of cereal is $0.24

Step-by-step explanation:

We are given the following information in the question:

Amount of cereals a box contain = 23.4 ounces

Cost of one box = $5.94

Cost of cereal per ounce =

Formula:

[tex]\text{Cost of one ounce of cereal} = \\\\\displaystyle\frac{\text{Cost of cereal}}{\text{Amount of cereal in a box}}[/tex]

Putting the values, we have:

[tex]\text{Cost of one ounce of cereal} = \displaystyle\frac{5.49}{23.4} = 0.2347 \approx 0.24[/tex]

Hence, the cost of one ounce of cereal is $0.24

Does 17/20 repeat or terminate

Answers

17/20  = 0.85

0.85 is a terminated decimal

hope this helps

Charles will babysit for up to 4 hours and charges $7 per hour. Write a function in function notation for this situation.

Answers

x hour and 7 dollars per hour

x = hour

7(x) is your function


thank you for Anlian for pointing it out.. there is 4 hours

so x = 4

plug in 4 in x. 7(4)

7 x 4 = 28

28 is your answer

hope this helps
well it actually you can tell the answer, the answer will be 4x7=28
If you mean by another way then is: X/7less than or equal to 4
well then is 7x=?

Plz help!!
Estimate each quotient using compatible numbers write what you estimated with like my answer is 7 and this is what I used 280÷4
Estimate these quotient round the numbers
1. 5564÷91 3.explain how to
2. 5391÷25 estimate 498÷12
4.which is the closest estimate for 2130÷ 33
A.7 B.17 C.70 D.700

Answers

1. 5564÷91
I know that 9 * 6 = 56
5564 rounds to 5600
91 rounds to 9
Since 56/9 = 6, then 5600/90 is the same as 560/9 = 60
The estimate is 60

2. 5391÷25
5391 sounds to 5400
25 is 1/4 of 100.
That means when you divide by 25, you can divide by 100 and multiply by 4.
5400/100 = 54
54 * 4 = 216
Estimate: 216

3. explain how to estimate 498÷12
48/12 = 4
498 is little more than 480, so 498/12 is little more than 40

4. which is the closest estimate for 2130÷ 33
A.7 B.17 C.70 D.700

2130/33
Round off the numerator and denominator to
2100/30
Reduce the fraction
210/3
Since I know that 21/3 = 7, then 210/3 = 70
Estimate: 70

Hello I'm Vanessa and I'm 16, im recently taking Geometry online and I'm trying to find someone that is willing to help me out. Thanks

Answers

What is your question?

MATH QUESTION DOWN BELOW

Answers

8/9+(-5/6)= 8/9-5/6 = 1/18
Therefore, 1/18/(1/6)
1/18*1/6 (cancel out)
your answer is 1/3

crystal's mother kept a record of. crystal's. height at different ages. she recorded the information in a table. is the relationship between crystal's age and her height proportional? explain.

Answers

No, Crystal's age and her height are not proportional. The ratios would have the numerators of 25 and 15, in order to be proportional, the numerators would need to be the same number.
Final answer:

The relationship between Crystal's age and her height is determined by examining the ratios of age to height for different entries in the table. If the ratios are equal, then the relationship is proportional.

Explanation:

To determine if the relationship is proportional, compare the ratios of Crystal's age to her height for different entries in the table. If the ratios are equal, then the relationship is proportional. If the ratios are not equal, then the relationship is not proportional.

For example, if Crystal's age is 10 and her height is 50 inches, the ratio would be 10/50 = 0.2. If Crystal's age is 20 and her height is 100 inches, the ratio would be 20/100 = 0.2. Since the ratios are equal, the relationship between Crystal's age and her height is proportional.

32 is the sum of a number z and 9

Answers

You can find out the answer by subtraction 32 by 9. This equals 23. 23 + 9 = 32. Therefore, z = 23. Hope this helps!
Z is 23.so you have to add 9 to 23 .ND YOU GET THE SIM OF 32

Max and Sheila are making orange juice. Max has mixed 15 cups of water with 4 cups of juice concentrate. Sheila has made her choose by mixing 8 cups water with 3 cups just concentrate.compare their ratios of juice concentrate to water using racial tables. State which beverage has a higher juice concentrate to water ratio.

Answers

so 15:4 and 8:3. 15:4 has a greater juice concentrate 

elliot drove 202.8 miles and used 6.5 gallons of gasoline.How many miles did he travel per gallon of gasoline?

Answers

I think the answer is 31.2 miles per gallon
First you need to do long division to divide 202.8 by 6.5. To help you with this you can just imagine that the decimals arent there. For instance:

202.8 = 2,028

6.5 = 65

So it will be easier for you to divide it then you add the decimals back in later.

If you solved it correctly you should have gotten 31.2.

I need help with 2x+12=3x-31

Answers

The value of x in the given equation is 41.

What is an equation?

An equation is a mathematical statement that shows that two mathematical expressions are equal.

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

For example, 3x + 5 = 15, 9x+9 = 9, 3x+9 = 7, ax+by = z etc.

Based on the degree, equations can be classified into the following three types: Linear equation, Quadratic equation or Cubic equation

Given that, an equation 2x+12 = 3x-31

Solving for x,

2x+12 = 3x-31

Combining the like terms, by transposing,

3x-2x = 31+12

x = 41

Hence, the value of x in the given equation is 41.

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