A man is standing 30 meters away from a tree. If the angle of elevation of the top of the tree from his eyes 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 of the top of the tree from his eyes 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 of the top of the tree from his eyes is 60 degrees, what is the height of the tree?
Step 1: Understand the problem. A man is standing 30 meters away from a tree and looking up at the top of the tree.
Step 2: Identify the angle of elevation. The angle at which the man looks up to see 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 (30 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 man to the tree).
Step 5: Write the formula. The formula is: height = distance * tan(angle). Here, distance = 30 meters and angle = 60 degrees.
Step 6: Calculate tan(60 degrees). The value of tan(60 degrees) is √3.
Step 7: Substitute the values into the formula. Height = 30 * tan(60 degrees) = 30 * √3.
