The length of KL is 103 feet, if ΔKLM, the measure of ∠M=90°, the measure of ∠L=55°, and LM = 59 feet.
Step-by-step explanation:
The given is,
ΔKLM
∠M= 90°
∠L= 55°
LM = 59 feet
Step:1
The given triangle KLM is right angle triangle,
Ref the attachment,
Trigonometric metric ratio for triangle KLM is,
[tex]cos[/tex] ∅ = [tex]\frac{Adj}{Hyp}[/tex]
For the triangle KLM sin ∅ becomes,
[tex]cos[/tex] ∅ = [tex]\frac{LM}{KL}[/tex].........................(1)
From the given,
∅ = 55°
LM = 59 feet
Equation (1) becomes,
[tex]cos[/tex] 55° = [tex]\frac{59}{x}[/tex]
Where [tex]cos[/tex] 55° = 0.5736,
0.5736 = [tex]\frac{59}{x}[/tex]
x = [tex]\frac{59}{0.5736}[/tex]
= 102.86
x = KL ≅ 103 feet
Step:2
Check for solution,
[tex]sin\alpha =\frac{Opp}{Hyp}[/tex]
For triangle KLM,
[tex]sin\alpha =\frac{LM}{KL}[/tex]
Substitute the values of LM and KL,
[tex]sin\alpha =\frac{59}{103}[/tex]
[tex]sin\alpha =0.57282[/tex]
[tex]\alpha = sin^{-1} 0.57282[/tex]
= 34.967
[tex]\alpha[/tex] ≅ 35°
For right angle triangle,
90° = ∅ + α
= 55° + 35°
90° = 90°
Result:
The length of KL is 103 feet, if ΔKLM, the measure of ∠M=90°, the measure of ∠L=55°, and LM = 59 feet.
