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A tree casts a shadow of 10 meters when the angle of elevation of the sun is 45
A tree casts a shadow of 10 meters when the angle of elevation of the sun is 45 degrees. What is the height of the tree?
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Practice Questions
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A tree casts a shadow of 10 meters when the angle of elevation of the sun is 45 degrees. What is the height of the tree?
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Height = shadow * tan(45) = 10 * 1 = 10 meters.
Questions & Step-by-step Solutions
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Q
Q: A tree casts a shadow of 10 meters when the angle of elevation of the sun is 45 degrees. What is the height of the tree?
Solution:
Height = shadow * tan(45) = 10 * 1 = 10 meters.
Steps: 6
Show Steps
Step 1: Understand that the angle of elevation is the angle between the ground and the line from the top of the tree to the sun.
Step 2: Know that when the angle of elevation is 45 degrees, the height of the tree and the length of the shadow are equal.
Step 3: Use the formula for height, which is height = shadow * tan(angle).
Step 4: Since the angle is 45 degrees, tan(45) equals 1.
Step 5: Substitute the values into the formula: height = 10 meters (shadow) * 1 (tan(45)).
Step 6: Calculate the height: height = 10 * 1 = 10 meters.
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