Question

The sun is 20º above the horizon. Find the length of a shadow cast by a park statue that is 16 feet tall. Approximate the answer to two decimal places. Show your work.

Answer 1

To find the shadow length of a 16-feet-tall statue with the Sun 20 degrees above the horizon, we use trigonometry. The length of the shadow is approximately 43.96 feet.

Step-by-step explanation:

The student's question is asking to find the length of a shadow cast by a 16-feet-tall park statue when the Sun is 20 degrees above the horizon. To solve this problem, we can use trigonometry, specifically the tangent function, which relates the angle of elevation of the Sun to the ratio of the opposite side (height of the statue) to the adjacent side (length of the shadow) in a right-angled triangle.

Step-by-Step Solution:

1. 
   
3. Set up the tangent function based on the angle of elevation: tan(20°) = height of statue / length of shadow.
4. 
   
6. Substitute the height of the statue (16 feet) into the equation: tan(20°) = 16 feet / length of shadow.
7. 
   
9. Solve for the length of the shadow: length of shadow = 16 feet / tan(20°).
10. 
    
12. Using a calculator, we find that tan(20°) ≈ 0.364, so the length of the shadow is approximately 16 feet / 0.364 ≈ 43.96 feet.

Therefore, the length of the shadow cast by the statue is approximately 43.96 feet when the Sun is 20 degrees above the horizon.