Question
A 4.5m tall tree casts a shadow 6m long. Find the angle of elevation of the sun at that time
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Answer to a math question A 4.5m tall tree casts a shadow 6m long. Find the angle of elevation of the sun at that time
Darrell
4.5100 Answers
Solution:
1. Given:
- The height of the tree is4.5 \, \text{m}
- The length of the shadow is6 \, \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
-\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 approximately36.87^\circ
1. Given:
- The height of the tree is
- The length of the shadow is
2. The angle of elevation of the sun can be found using the tangent function in a right triangle:
-
- 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:
-
4. Find the angle
-
5. Calculate
- Using a calculator,
6. Therefore, the angle of elevation of the sun is approximately
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