CPM Homework Help : CCG Problem 4-113

Kamillah decided to find the height of the Empire State Building. She walked $1$ mile away ( $5280$ feet) from the tower and found that she had to look up $15.5^{\large \circ }$ to see the top. Assuming Manhattan is flat, if Kamillah’s eyes are $5$ feet above the ground how tall is the Empire State Building?

Step 1:

Draw a diagram to help solve this problem.

Step 2:

$\text{tan}(15.5º) = \frac{\textit{x}}{5280}$

Hint:

Don't forget that $x$ is $5$ feet off the ground.

Horizontal line with vertical rectangle on the right side, Above the line is Right triangle, vertical leg, labeled x, is top part of rectangle, horizontal leg, labeled 5280 feet = 1 mile, angle opposite vertical leg, labeled 15.5 degrees, distance between that vertex & horizontal line is labeled, 5 feet above ground.