A building 71.42 feet tall has a shadow that is 74.77 feet long. Find the angle of elevation of the sun to the nearest hundredth of a degree.

To find the angle of elevation of the sun, we can use trigonometry, specifically the tangent function. The angle of elevation (\(\theta\)) is the angle formed between the top of the building, the end of the shadow, and the ground. 

The formula is:
\[
\tan(\theta) = \frac{{\text{{height of the building}}}}{{\text{{length of the shadow}}}}
\]

Given:
- Height of the building = 71.42 feet
- Length of the shadow = 74.77 feet

We can solve for \(\theta\) by taking the arctangent (inverse tangent) of the ratio.

\[
\theta = \tan^{-1}\left(\frac{71.42}{74.77}\right)
\]

Now, let's calculate the angle of elevation.

\[
\theta = \tan^{-1}(0.9552) \approx 43.56^\circ
\]

So, the angle of elevation of the sun is approximately **43.56°**.

Would you like more details on the calculation or any clarifications?

Here are 5 related questions to explore further:
1. What is the relationship between angle of elevation and the length of shadows?
2. How does the height of the building affect the angle of elevation?
3. How can you calculate the height of a building if you know the angle of elevation and shadow length?
4. How do you find the angle of elevation when dealing with non-right-angle triangles?
5. What other trigonometric functions can be used in elevation and shadow problems?

**Tip:** When solving for angles in trigonometry, always make sure your calculator is set to the correct mode (degrees or radians).

Learn how to calculate the angle of elevation of the sun using trigonometry for a building 71.42 feet tall with a shadow length of 74.77 feet. This problem covers key trigonometric concepts like tangent ratios and inverse functions, suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation