The angle of elevation of the top of a tower at a point X is 30°. On walking 30 m towards the tower if the angle of elevation becomes 60° at point Y, find the height of the tower?

Sure, let's solve this step by step.

Step 1: Understand the problem We have a tower and two points X and Y. At point X, the angle of elevation to the top of the tower is 30°. When we move 30m closer to the tower at point Y, the angle of elevation becomes 60°. We need to find the height of the tower.

Step 2: Draw a diagram It's always helpful to draw a diagram for such problems. Draw the tower as a vertical line. Mark the points X and Y on a horizontal line, with Y being closer to the tower. Draw lines from X and Y to the top of the tower, forming two right triangles.

Step 3: Use trigonometry In right triangle XYT (where T is the top of the tower), we can use the tangent of the angle to find the height of the tower (h). The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side.

So, tan(60°) = h / 30m => h = 30m * tan(60°) => h = 30m * √3 => h = 30√3 m

So, the height of the tower is 30√3 meters.