A man standing on the ground observes the top of a hill at an angle of elevation of 30 degrees. If he is 100 m away from the base of the hill, what is the height of the hill? (2022)
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A man standing on the ground observes the top of a hill at an angle of elevation of 30 degrees. If he is 100 m away from the base of the hill, what is the height of the hill? (2022)
Q: A man standing on the ground observes the top of a hill at an angle of elevation of 30 degrees. If he is 100 m away from the base of the hill, what is the height of the hill? (2022)
Step 1: Understand that the man is looking at the top of the hill from a distance of 100 meters.
Step 2: The angle of elevation from the man's eyes to the top of the hill is 30 degrees.
Step 3: To find the height of the hill, we can use the tangent function from trigonometry, which relates the angle to the opposite side (height) and the adjacent side (distance).
Step 4: The formula to find the height (h) is: height = distance * tan(angle).
Step 5: Plug in the values: height = 100 m * tan(30 degrees).
Step 6: Calculate tan(30 degrees), which is equal to 1/√3 (approximately 0.577).
Step 7: Now calculate the height: height = 100 m * (1/√3).
Step 8: This simplifies to approximately 100 m * 0.577 = 57.7 m.
Step 9: Therefore, the height of the hill is approximately 25 m.
