A man is standing 30 meters away from a tower. If the angle of elevation of the top of the tower from the man's position is 30 degrees, what is the height of the tower?
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A man is standing 30 meters away from a tower. If the angle of elevation of the top of the tower from the man's position is 30 degrees, what is the height of the tower?
Q: A man is standing 30 meters away from a tower. If the angle of elevation of the top of the tower from the man's position is 30 degrees, what is the height of the tower?
Step 1: Understand the problem. A man is standing 30 meters away from a tower and looking up at the top of the tower at an angle of 30 degrees.
Step 2: Identify the right triangle formed by the man, the top of the tower, and the base of the tower. The distance from the man to the tower is the base of the triangle.
Step 3: The height of the tower is the opposite side of the triangle, and the distance from the man to the tower is the adjacent side.
Step 4: Use the tangent function, which relates the angle of elevation to the opposite and adjacent sides of the triangle. The formula is: tan(angle) = opposite/adjacent.
Step 5: Rearrange the formula to find the height (opposite side): height = distance * tan(angle).
Step 6: Substitute the values into the formula: height = 30 meters * tan(30 degrees).
Step 7: Calculate tan(30 degrees). The value of tan(30 degrees) is 1/√3.
Step 8: Now calculate the height: height = 30 * (1/√3).
