A statue stands on the top of a 25m tall pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60ºand from the same point, the angle of elevation of the top of the pedestal is 45º. Find the height of the statue?Options20(√3-1)15(√3+1)10(√3+1)25(√3-1)
Question
A statue stands on the top of a 25m tall pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60ºand from the same point, the angle of elevation of the top of the pedestal is 45º. Find the height of the statue?Options20(√3-1)15(√3+1)10(√3+1)25(√3-1)
Solution
To solve this problem, we can use the tangent of the angles of elevation, which is the ratio of the opposite side (height) to the adjacent side (distance from the point on the ground to the pedestal).
Let's denote:
- the height of the statue as h,
- the height of the pedestal as p = 25m,
- the distance from the point on the ground to the pedestal as d.
From the problem, we know two equations based on the tangent of the angles of elevation:
-
tan(45º) = p/d => d = p/tan(45º) = 25m (since tan(45º) = 1)
-
tan(60º) = (p + h)/d => h = d*tan(60º) - p
Substituting d from equation 1) into equation 2), we get:
h = 25mtan(60º) - 25m = 25m(√3 - 1)
So, the height of the statue is 25m*(√3 - 1), which corresponds to option 4: 25(√3-1).
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