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 (which is given as 25m), and the distance from the point on the ground to the pedestal as d.

From the problem, we have two equations based on the tangent of the angles:

1) tan(45º) = p/d = d = p/tan(45º) = 25m (since tan(45º) = 1)

2) tan(60º) = (p+h)/d = d = (p+h)/tan(60º)

Since the distance d is the same in both equations, we can set them equal to each other and solve for h:

25m = (25m + h)/√3 = 25√3 = 25 + h = h = 25√3 - 25

Therefore, the height of the statue is 25(√3 - 1) meters. So, the correct option is 25(√3 - 1).

Question

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 (which is given as 25m), and the distance from the point on the ground to the pedestal as d.

From the problem, we have two equations based on the tangent of the angles:

1) tan(45º) = p/d => d = p/tan(45º) = 25m (since tan(45º) = 1)

2) tan(60º) = (p+h)/d => d = (p+h)/tan(60º)

Since the distance d is the same in both equations, we can set them equal to each other and solve for h:

25m = (25m + h)/√3 => 25√3 = 25 + h => h = 25√3 - 25

Therefore, the height of the statue is 25(√3 - 1) meters. So, the correct option is 25(√3 - 1).

Knowee AI · Accepted Answer

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 (which is given as 25m), and the distance from the point on the ground to the pedestal as d.

From the problem, we have two equations based on the tangent of the angles:

1) tan(45º) = p/d => d = p/tan(45º) = 25m (since tan(45º) = 1)

2) tan(60º) = (p+h)/d => d = (p+h)/tan(60º)

Since the distance d is the same in both equations, we can set them equal to each other and solve for h:

25m = (25m + h)/√3 => 25√3 = 25 + h => h = 25√3 - 25

Therefore, the height of the statue is 25(√3 - 1) meters. So, the correct option is 25(√3 - 1).

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?Options10(√3+1)25(√3-1)20(√3-1)15(√3+1)

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