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

Answer:

it's 102.9

Step-by-step 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.

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.