TRIGONOMETRY, degrees and measurements

Question

For safety reasons, the angle a ladder makes with the ground should be no greater than 66°. Find the length to the nearest foot of the shortest ladder that will safely reach a roof that is 25 feet high.

Round to the nearest foot.

The length of the ladder is  ?  feet.

Answer 1

The ladder against the build forms a right triangle. Let x be the length of the ladder.

sin(66°) = height/hypotenuse = 25/x

x = 25/sin(66°) = 27.37 ft