Final answer:
To find the angle of elevation of the sun, one should use the tangent trigonometric ratio on a right triangle formed by the flagpole and its shadow. The correct answer is not given in option.
Step-by-step explanation:
The question is asking to find the angle of elevation of the sun given a 40-foot flagpole that casts a 25-foot shadow. To solve this problem, we'll use trigonometric ratios—specifically, tangent, since we are dealing with a right-angled triangle formed by the flagpole, its shadow, and the line of sight from the top of the flagpole to the tip of the shadow.
Step-by-Step Solution
- Identify the lengths: the opposite side (the flagpole) is 40 feet, and the adjacent side (the shadow) is 25 feet.
- Use the tangent ratio: tan(θ) = opposite / adjacent, which translates to tan(θ) = 40 / 25.
- Calculate the arctangent (inverse tangent) to find the angle θ: θ = arctan(40 / 25).
- Use a calculator to find θ, which gives you the angle of elevation of the sun. In this case, θ is approximately 58°. However, since this angle is not one of the provided choices, there might be an error in the question or the answer choices. Likely, you’d be expected to choose the angle closest to the one you calculated, which would likely be optionl 60°.
It is important to note that the sun's angle of elevation changes throughout the day; therefore, these calculations are only accurate at the moment the shadow is observed.