Trigonometry Math Word Problem

Question

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.

Answer 1

Two ways to do it.

 

The easy way is to use the Pythagorean Theorem, a² + b² = c².  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.