Tobius is going to climb a ladder to reach and fix a piece of siding located 30 feet above the ground on the building. if he places the ladder at a 60° angle with the ground, about how long is the ladder?

Check the picture.

Let BC represent the wall, AC the ladder and AB the distance of the feet of the ladder to the wall.

ABC form a right triangle, with m(B)=90°, m(A)=60° and m(C)=30°.

AB is the side opposite the angle 30°, so the length of AB is half of the length of the hypotenuse AC.

Thus, let |AC|=2x, and |AB|=x.

By the Pythagorean theorem:









thus 

the length of the ladder is feet

feet