A 4.5m tall tree casts a shadow 6m long. Find the angle of elevation of the sun at that time

Solution:
1. Given:
- The height of the tree is 4.5 \, \text{m}.
- The length of the shadow is 6 \, \text{m}.

2. The angle of elevation of the sun can be found using the tangent function in a right triangle:
- \text{tan}(\theta) = \frac{\text{opposite side}}{\text{adjacent side}}
- In this case, the opposite side is the height of the tree, and the adjacent side is the length of the shadow.

3. Calculate the tangent of the angle:
- \text{tan}(\theta) = \frac{4.5}{6} = 0.75

4. Find the angle \theta using the inverse tangent (arctan) function:
- \theta = \arctan(0.75)

5. Calculate \theta:
- Using a calculator, \theta \approx 36.87^\circ.

6. Therefore, the angle of elevation of the sun is approximately 36.87^\circ.