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s2008m [1.1K]
3 years ago
8

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.

Mathematics
2 answers:
tigry1 [53]3 years ago
5 0

Answer:

it's 102.9

Step-by-step explanation:

Travka [436]3 years ago
4 0

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.

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