Mathematics, 13.04.2020 22:38 Miccyy

In ΔKLM, the measure of ∠M=90°, the measure of ∠L=55°, and LM = 59 feet. Find the length of KL to the nearest tenth of a foot.

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Answer from: nawaphon1395

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,

cos ∅ = $\frac{Adj}{Hyp}$

For the triangle KLM sin ∅ becomes,

cos ∅ = $\frac{LM}{KL}$ .........................(1)

From the given,

∅ = 55°

LM = 59 feet

Equation (1) becomes,

cos 55° = $\frac{59}{x}$

Where cos 55° = 0.5736,

0.5736 = $\frac{59}{x}$

x = $\frac{59}{0.5736}$

= 102.86

x = KL ≅ 103 feet

Step:2

Check for solution,

$sin\alpha =\frac{Opp}{Hyp}$

For triangle KLM,

$sin\alpha =\frac{LM}{KL}$

Substitute the values of LM and KL,

$sin\alpha =\frac{59}{103}$

$sin\alpha =0.57282$

$\alpha = sin^{-1} 0.57282$

= 34.967

$\alpha$ ≅ 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.

In ΔKLM, the measure of ∠M=90°, the measure of ∠L=55°, and LM = 59 feet. Find the length of KL to th

Answer from: Quest

16 minutes is correct

Answer from: Quest

it could 14.28 but if its not that one then it has to be the 17 one. hope this ! : )

step-by-step explanation:

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In ΔKLM, the measure of ∠M=90°, the measure of ∠L=55°, and LM = 59 feet. Find the length of KL to th...