CPM Homework Help : INT2 Problem 5-116

Kamillah decides to calculate the height of the Empire State Building. She walks $1$ mile ( $5280$ feet) away from the tower and finds that she has to look up $15.5^\circ$ 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:

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

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.