From a point 375 meters away from the foot of a tower, the top of the tower is observed at an angle of elevation of 45deg, then the height (in meters) of the tower is?
Question
From a point 375 meters away from the foot of a tower, the top of the tower is observed at an angle of elevation of 45deg, then the height (in meters) of the tower is?
Solution
To solve this problem, we can use the tangent of the angle of elevation, which is the ratio of the opposite side (the height of the tower) to the adjacent side (the distance from the tower).
The formula for tangent is:
tan(θ) = opposite/adjacent
Given that the angle of elevation (θ) is 45 degrees and the distance from the tower (adjacent) is 375 meters, we can plug these values into the formula:
tan(45) = height/375
Since the tangent of 45 degrees is 1, the equation simplifies to:
1 = height/375
Solving for height, we get:
height = 375 meters
So, the height of the tower is 375 meters.
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