Given:
- KLMN is a trapezoid
- KL = MN
- LN = √(89)
- LH: altitude
- LM = 3
- KN = 13
Find: m∠LKN
See attached image.
Answers
Answer:
45 degrees
Step-by-step explanation:
If KL = MN, and LM =3 and KN = 13, then HN = 13 - (13-3)/2 = 8
LN = sqrt(HN^2 + LH^2) -->
LN = sqrt89 sqrt(8^2 + LH^2) -->
89 = 64 + LH ^2 -->
25 = LH^2 -->
LH = 5
Because HN = 8, HK = 13 - 8 = 5
That makes both legs equal, which makes m∠LKN = 45 degrees
The angle m∠LKN is equal to 45 degrees.
To understand more, check below explanation.
Trapezoid :It is given that,
KL = MN, LM =3 , KN = 13 and LN [tex]=\sqrt{89}[/tex]
So that, HN = 13 - (13-3)/2 = 13 - 5 = 8
[tex]LN = \sqrt{(HN)^{2}+(LH)^{2} }\\\\\sqrt{89} = \sqrt{(8)^{2}+(LH)^{2} }\\\\89=64+(LH)^{2} \\\\LH=\sqrt{25}=5[/tex]
Since, HN = 8. So that, HK = 13 - 8 = 5
In a triangle, if two sides are equal. Then, opposite angle of both sides are also equal.
In triangle LKH, LH = HK = 5 and [tex]\angle H=90[/tex]
So that, m∠LKN = 90/2 = 45 degree.
Hence, the angle m∠LKN is equal to 45 degrees.
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