From a point P on a level ground, the angle of elevation of the top tower is 30deg. If the tower is 100 m high, the distance of point P from the foot of the tower is
Question
From a point P on a level ground, the angle of elevation of the top tower is 30deg. If the tower is 100 m high, the distance of point P from the foot 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 point to the tower).
The formula for tangent is:
tan(θ) = opposite/adjacent
We know that the angle of elevation (θ) is 30 degrees and the height of the tower (opposite) is 100m. We want to find the distance from the point to the tower (adjacent), which we'll call d.
So we can set up the equation as follows:
tan(30) = 100/d
To solve for d, we rearrange the equation:
d = 100/tan(30)
Using a calculator, we find that tan(30) is approximately 0.577. So:
d = 100/0.577
d = 173.21 meters
So, the distance of point P from the foot of the tower is approximately 173.21 meters.
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