Question

the proper angle for a ladder is about 75 degrees. from the ground. suppose you have a 9 foot ladder. how far from the house should you place the base of the ladder ? round answer to at least 2 decimal places

Answer 1

ANSWER:

2.33 foot

STEP-BY-STEP EXPLANATION:

We can calculate the distance from the staircase to the wall, by means of the trigonometric cosine ratio, which is the following:

$\begin{gathered} \cos \theta=\frac{\text{ adjacent}}{\text{ hypotenuse}} \\ \theta=75\text{\degree} \\ \text{ hypotenuse = 9 foot} \\ \text{adjacent = x} \end{gathered}$

Replacing and solving for x:

$\begin{gathered} \cos 75=\frac{x}{9} \\ x=9\cdot\cos 75 \\ x=2.33 \end{gathered}$

The distance would be 2.33 foot