Question

Isaiah wants to know the height of a water tower. He measures the shadow of the watertower and finds that it is 16 meters long. Isaiah also knows that a nearby cell phone towerthat is 45 meters tall is casting a shadow 24 meters long. How tall is the water tower?

Answer 1

Since the rays of the sun are seemingly parallel as seen from Earth, the corresponding sides of the triangles are proportional.

This means that:

$\frac{x}{16m}=\frac{45m}{24m}$

Multiply both sides by 16 m to find the height x:

$x=\frac{45m}{24m}\cdot16m$

Simplify the expression on the right hand side of the equation:

$x=30\text{ m}$

Therefore, the water tower is 30 m tall.