A man is standing 30 meters away from a tree. If the angle of elevation from his eyes to the top of the tree is 60 degrees, what is the height of the tree?
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A man is standing 30 meters away from a tree. If the angle of elevation from his eyes to the top of the tree is 60 degrees, what is the height of the tree?
Q: A man is standing 30 meters away from a tree. If the angle of elevation from his eyes to the top of the tree is 60 degrees, what is the height of the tree?
Step 1: Understand the problem. We have a man standing 30 meters away from a tree, and we need to find the height of the tree using the angle of elevation.
Step 2: Identify the angle of elevation. The angle given is 60 degrees.
Step 3: Recall the relationship between the height of the tree, the distance from the man to the tree, and the angle of elevation. We can use the tangent function: tan(angle) = height / distance.
Step 4: Rearrange the formula to find the height: height = distance * tan(angle).
Step 5: Substitute the known values into the formula. The distance is 30 meters and the angle is 60 degrees: height = 30 * tan(60 degrees).
Step 6: Calculate tan(60 degrees). The value of tan(60 degrees) is √3, which is approximately 1.732.
Step 7: Multiply the distance by the value of tan(60 degrees): height = 30 * √3 = 30 * 1.732.
Step 8: Perform the multiplication: height = 51.96 meters.
