Final answer:
Using the tangent function with an angle of elevation of 35.0° and a shadow length of 66.0ft, the height of the tower is approximately 46.21 feet.
Step-by-step explanation:
To solve the mathematical problem completely and find the height of the vertical tower, when the shadow is 66.0ft long and the angle of elevation of the sun is 35.0°, we can use trigonometry. Specifically, we employ the tangent function which relates the angle of elevation to the ratio of the opposite side (height of the tower) to the adjacent side (length of the shadow).
We know that:
- Tangent of an angle θ = Opposite side / Adjacent side
- Tan(35.0°) = Height of the tower / 66.0ft
Using this equation:
- Height of the tower = Tan(35.0°) × 66.0ft
Now, we calculate the tangent of 35.0° using a calculator and then multiply by 66.0 to find the height:
Height of the tower = 0.7002 × 66.0ft
Height of the tower ≈ 46.21ft
Therefore, the height of the tower is approximately 46.21 feet.