Question

A roofer props a ladder against a wall so that the top of the ladder reaches a 30-foot roof that needs repair. If the angle of elevation from the bottom of the ladder to the roof is 55°, how far is the ladder from the base of the wall? Round your answer to the nearest foot.

Answer 1

Set this up like a right triangle with the height of the triangle as 30, the angle across from that side, the reference angle, as 55, and the base is your unknown, x.  This means that we have the angle, the side across from it, and the side adjacent to it.  That sounds like the tangent ratio to me!  Tangent of the angle is the side opposite over the side adjacent: $tan(55)= \frac{30}{x}$.  Solving for x: $x= \frac{30}{tan(55)}$.  Do that on your calculator in degree mode to get that the distance between the base of the ladder and the wall is 21 feet