Question

Pam is placing a bird feeder in a tree in her back yard. She first needs to put up a 10-inch wooden platform in the fork of two tree branches that make a 52° angle, as shown below. What equation can Pam use to determine xthe distance up the tree trunk from the fork at she should drill attach the platform?

Answer 1

Answer:

$x = \frac{10}{\tan(52^o)}$

Step-by-step explanation:

Given

See attachment for illustration

Required

Equation to find x

The relationship between angle $52^o$ and side lengths x and 10 inches is by tangent formula which is given by:

$\tan(\theta) = \frac{Opposite}{Adjacent}$

So, we have:

$\tan(52^o) = \frac{10}{x}$

Make x the subject

$x = \frac{10}{\tan(52^o)}$