Question

the directions for assembling the pool state that the ladder should be placed at an angle of 65° relative to level ground. the height of the pool is 7 feet. which of the following expressions gives the distance, in feet, that the bottom of the ladder should be placed away from the bottom edge of the pool in order to comply with the directions?
a $\frac{7}{sin 65^{circ}}$
b $\frac{7}{\tan 65^{circ}}$
c $\frac{65}{\tan 7^{circ}}$
d $\frac{\tan 65^{circ}}{7}$
e $7 \tan 65^{circ}$

Explanation:

Step1: Recall the tangent function

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, the height of the pool (\(7\) feet) is the opposite side, and the distance \(x\) from the bottom of the ladder to the bottom edge of the pool is the adjacent side, and \(\theta = 65^{\circ}\).
So, \(\tan65^{\circ}=\frac{7}{x}\).

Step2: Solve for \(x\)

Cross - multiply the equation \(\tan65^{\circ}=\frac{7}{x}\) to get \(x\tan65^{\circ}=7\). Then, \(x = \frac{7}{\tan65^{\circ}}\).

Answer:

B. \(\frac{7}{\tan65^{\circ}}\)