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 $x$:
$tan(69)= \frac{14}{x}$
$x= \frac{14}{tan(69)}$
$x=5.4$

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-