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

step-by-step explanation:

If you dont know the correct answer, just ignore this question

Answer from: Quest

At a constant it will take one hour to travel 32 mi.at that speed it will take 1/2 hr to travel the remaining 16 mi.it will take 1+1/2 hr to travel the 48mi @ 32mph.so 1 hr = 60 min& 1/2 hr = 30 min1+1/2 hr = 90 min.there are 60s in each 90 × 60 = 3600 seconds.the real question seriously is he why are they driving so slow? ! lol.

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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...

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