Christina wants to know the height of a radio tower. She measures the shadow of the radio tower and finds that it is 45 yards long. Christina also knows that a nearby monument that is 16 yards tall is casting a shadow 30 yards long. How tall is the radio tower? Write your answer as a whole number or a decimal. Do not round.

To determine the height of the radio tower, we can use the concept of similar triangles. Here's how: 1. **Identify the Known Values:** - **Monument Height:** 16 yards - **Monument Shadow:** 30 yards - **Radio Tower Shadow:** 45 yards 2. **Set Up the Proportion:** Since the sun's rays are consistent, the ratio of the height to the shadow length will be the same for both the monument and the radio tower. \[ \frac{\text{Height of Monument}}{\text{Shadow of Monument}} = \frac{\text{Height of Radio Tower}}{\text{Shadow of Radio Tower}} \] Plugging in the known values: \[ \frac{16}{30} = \frac{h}{45} \] 3. **Solve for \( h \) (Height of Radio Tower):** \[ h = \frac{16}{30} \times 45 \] Simplify the calculation: \[ h = \frac{16 \times 45}{30} = \frac{720}{30} = 24 \] **Answer:** The radio tower is **24** yards tall.