Question

A ladder is leaning against a house so that the top of the ladder is 12 feet above the ground. The angle the ladder makes with the ground is 51°. How long is the ladder?

12•sin51°
12/cos51°
12•cos51°
12/sin51°
None of these

Answer 1

12/sin5°

Explanation:

This angle can be calculated using the law of sine:

sin(angle)=opposite cathete/hypothenuse

sin(angle)=wall/ladder

In this exercise we want to calculate the length of the hypotenuse (ladder), so the equation is changed afterwards.

sin(angle)=wall/ladder

sin(angle)*ladder=wall

ladder=wall/sin(angle)

Now the given values are used:

ladder=wall/sin(angle)

ladder=12ft/cos(51°)