Question

A ladder is leaned against a wall that is six feet tall, so that the top of the ladder is resting on the top
of the wall. The ladder is inclined at an angle of thirty degrees. Find the distance from the bottom of
the ladder to the base of the wall. Round your answer to the nearest tenth of a foot. Do not include
units in your answer.

Answer 1

Answer:

$10.4$

Step-by-step explanation:

The ladder leaning against the wall forms a right triangle with the wall and the ground. Therefore, we can use basic trig for a right triangle to solve this problem.

In a right triangle, $\tan\theta=\frac{\text{opp}}{\text{adj}}$. Therefore, we have the following equation, where $x$ is distance between the bottom of the ladder to the base of the wall:

$\tan 30^{\circ}=\frac{6}{x},\\x=\frac{6}{\tan 30^{\circ}},\\x\approx \boxed{10.4}$.