Right angle Trig

Question

The roof of a particular house is 25 feet above the ground. For safety reasons, the angle that a ladder makes with the ground should be no greater than 70 degrees. What is the length of the shortest ladder that will reach the roof of the house safely?

Answer 1

Since the building is not the Leaning Tower of Pisa, it is best to think about this in terms of a right triangle. We're trying to find the minimum length of the hypotenuse such that one of the interior angles is 70-degrees. We're given one of the sides opposite the 70-degree angle to be 25-feet. Now, draw a right triangle. For the interior angles, we have two angles of 90 and 70 degrees. This means that the top angle is 20-degrees, as all angles of the triangle must add up to 180-degrees. Then, we can find a trig. relationship to calculate the hypotenuse length.

sin(Θ) = Opp/Hyp. Thus, sin(70) = 25/H. Through some straightforward algebraic manipulation, we find the minimum required hypotenuse (ladder) length to be

H = 25/sin(70).

(Make sure your calculator is in degrees.)