A person is standing on the ground and looking at the top of a tree. If the angle of elevation is 60 degrees and the person is 20 meters away from the tree, what is the height of the tree?
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A person is standing on the ground and looking at the top of a tree. If the angle of elevation is 60 degrees and the person is 20 meters away from the tree, what is the height of the tree?
Q: A person is standing on the ground and looking at the top of a tree. If the angle of elevation is 60 degrees and the person is 20 meters away from the tree, what is the height of the tree?
Step 1: Understand the problem. You have a person looking at the top of a tree from a distance of 20 meters.
Step 2: Identify the angle of elevation. The angle at which the person looks up to the top of the tree is 60 degrees.
Step 3: Recall the relationship between the height of the tree, the distance from the tree, and the angle of elevation. This can be calculated using the tangent function.
Step 4: Write down the formula for height: Height = distance * tan(angle).
Step 5: Substitute the known values into the formula: Height = 20 * tan(60 degrees).
Step 6: Calculate tan(60 degrees). The value of tan(60 degrees) is √3.
Step 7: Multiply the distance by the value of tan(60 degrees): Height = 20 * √3.
