Question

A ladder needs to reach a second-story window that is 14 feet above the ground and make an angle with the ground of 69°. How far out from the building does the base of the ladder need to be positioned? Round your answer to the nearest tenth.

Answer 1

Lets build a right triangle with the information provided in the problem. We know that the ground and the ladder make an angle of 69°.We also know that the ladder needs to reach a second-story window that is 14 feet, so the opposite side from the angle of our triangle will measure 14 ft. Finally, let
`x` represents the distance between the building and the base of the ladder.

Now that we have our triangle, we will use a trigonometric function to relate its angle with its opposite and adjacent sides. That function is tangent. So lets use it to find
`x`:

`tan(69)= (14)/(x)`

`x= (14)/(tan(69))`

`x=5.4`

We can conclude that for the ladder to reach 14 feet in the building, its base must be 5.4 feet away from the base of the building-