A ladder is leaning against a building and makes 42° angle with the ground. The top of the ladder reaches 30 feet up on the building. What is the length of the ladder?

Here we have a right triangle with hypotenuse h, which is to be found. The top of the ladder is 30 feet above the ground, and that distance is opposite the 42 degree angle mentioned. Use the sine function to determine the hypotenuse, h:

sin 42 deg = opp / hyp, or hyp*sin 42 deg = 30 ft. Then hyp = (30 ft) (sin 42), which in turn equals hyp = (30 ft) / (0.669) = 44.8 feet (answer)