A man is standing on the ground and looking at the top of a tree. If the angle of elevation is 60 degrees and he is 10 meters away from the base of the tree, what is the height of the tree?
Practice Questions
1 question
Q1
A man is standing on the ground and looking at the top of a tree. If the angle of elevation is 60 degrees and he is 10 meters away from the base of the tree, what is the height of the tree?
5√3 m
10√3 m
15√3 m
20√3 m
Using tan(60°) = height/10, we have √3 = height/10. Therefore, height = 10√3 m.
Questions & Step-by-step Solutions
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Q
Q: A man is standing on the ground and looking at the top of a tree. If the angle of elevation is 60 degrees and he is 10 meters away from the base of the tree, what is the height of the tree?
Solution: Using tan(60°) = height/10, we have √3 = height/10. Therefore, height = 10√3 m.
Steps: 8
Step 1: Understand the problem. A man is looking at the top of a tree from a distance of 10 meters.
Step 2: Identify the angle of elevation. The angle at which he looks up to the top of the tree is 60 degrees.
Step 3: Visualize the situation. Imagine a right triangle where one side is the height of the tree, the other side is the distance from the man to the tree (10 meters), and the angle between the ground and the line of sight to the top of the tree is 60 degrees.
Step 4: Use the tangent function. In a right triangle, the tangent of an angle is the opposite side (height of the tree) divided by the adjacent side (distance from the tree). So, tan(60°) = height / 10.
Step 5: Find the value of tan(60°). The value of tan(60°) is √3.
Step 6: Set up the equation. Now we have √3 = height / 10.
Step 7: Solve for height. Multiply both sides by 10 to get height = 10√3.
Step 8: Calculate the height. The height of the tree is 10√3 meters.
