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).