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Rudy is trying to estimate the height of the water tower next to his school. To do so, he looks out of a...

Rudy is trying to estimate the height of the water tower next to his school. To do so, he looks out of a second-story window, 225 meters from the water tower. Rudy's line of sight to the top of the water tower makes a 21° angle of elevation, and his line of sight to the base of the water tower makes a 4° angle of depression.
What is the height of the water tower?
Round your answer to the nearest whole number.

Answer

The tower’s height is the sum of the distances above and below the window’s horizontal level:

h = 225 tan(21°) + 225 tan(4°) ≈ 86.37 + 15.73 = 102.10 meters.

Rounded to the nearest whole number, the water tower is 102 meters tall.

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