Question

A 10-foot ramp must make an angle of 30° with the ground if it is to reach a certain window. What angle must a 15-foot ramp make with the ground to reach the same window?

Answer 1

19.5

Explanation:

Answer 2

In solving problems like this, it's best to work on a diagram (see attached image). First, given the angle formed by the ramp and the length of the ramp, we can apply the properties of right triangles and recall that


`sin \theta = (opposite)/(hypotenuse)`

Hence, we have


`\sin 30^(0) = (h)/(10)`

`(1)/(2) = (h)/(10)`

`h = 5`

Now that we have the window's height, we can compute for the angle, θ, if the ramp has a length of 15.


`\sin \theta = (5)/(15)`

`\theta = \sin^(-1)((1)/(3))`

`\theta = 19.47`

Therefore, for the 15-foot ramp to reach the window, the ramp must form an angle of 19.47°.

Answer: 19.47°