Question

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.

Answer 1

it's 102.9

Explanation:

Answer 2

The length of KL is 103 feet, if ΔKLM, the measure of ∠M=90°, the measure of ∠L=55°, and LM = 59 feet.

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` ∅ =
`(Adj)/(Hyp)`

For the triangle KLM sin ∅ becomes,

`cos` ∅ =
`(LM)/(KL)`.........................(1)

From the given,

∅ = 55°

LM = 59 feet

Equation (1) becomes,

`cos` 55° =
`(59)/(x)`

Where
`cos` 55° = 0.5736,

0.5736 =
`(59)/(x)`

x =
`(59)/(0.5736)`

= 102.86

x = KL ≅ 103 feet

Step:2

Check for solution,

`sin\alpha =(Opp)/(Hyp)`

For triangle KLM,

`sin\alpha =(LM)/(KL)`

Substitute the values of LM and KL,

`sin\alpha =(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.