Samantha S.

asked • 05/16/18# Trigonometry Math Word Problem

I've tried to solve the math problem. When I draw the diagram, it looks like I have to use the Cosine. However, I don't have an angle degree. I think I've missed a step somewhere. Wouldn't I have to solve the angle first? I've either confused myself or misunderstood the question.

Calculate the length of a staircase that is 3.2 m high, and has a slanted height of 4.7 m.

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## 1 Expert Answer

Philip P. answered • 05/16/18

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Two ways to do it.

The easy way is to use the Pythagorean Theorem, a

^{2}+ b^{2}= c^{2}. In your problem, b = 3.2 and c = 4.7. Solve for a, the length of the staircase.With trig, note that the angle of the staircase can be found using inverse trig functions. Specifically:

θ = sin

^{-1}(3.2/4.7)Use you calculator to get the answer. Th length of the staircase will be:

cos(θ) = length/hypotenuse

cos(θ) = length/4.7

Solve for length.

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Samantha S.

05/16/18