A man is standing at a distance of 50 meters from a tower. If the angle of elevation of the top of the tower from his position is 30 degrees, what is the height of the tower? (2021)
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A man is standing at a distance of 50 meters from a tower. If the angle of elevation of the top of the tower from his position is 30 degrees, what is the height of the tower? (2021)
Q: A man is standing at a distance of 50 meters from a tower. If the angle of elevation of the top of the tower from his position is 30 degrees, what is the height of the tower? (2021)
Step 1: Understand the problem. A man is standing 50 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, and the height of the tower is the vertical side.
Step 3: Recall the definition of the tangent function in a right triangle. The tangent of an angle is equal to the opposite side (height of the tower) divided by the adjacent side (distance from the man to the tower).
Step 4: Write the formula for height using the tangent function: Height = distance * tan(angle).
Step 5: Substitute the known values into the formula: Height = 50 * tan(30 degrees).
Step 6: Calculate tan(30 degrees). The value of tan(30 degrees) is 1/√3.
Step 7: Substitute tan(30 degrees) into the formula: Height = 50 * (1/√3).
Step 8: Simplify the expression: Height = 50/√3.
Step 9: If needed, calculate the approximate height by evaluating 50/√3, which is about 25 meters.
