The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower, is 30°. Find the height of the tower.
The height of the tower is 10 m.
Explanation
This problem is solved using the application of trigonometry, specifically the tangent ratio, similar to the approach seen in Example 5 and Question 11 of the provided context. We treat the situation as a right-angled triangle where the tower is the perpendicular side and the distance on the ground is the base. Since the angle of elevation and the distance are given, we use the tangent of the angle to find the height of the tower.
Solution Steps
Step 1: Let AB be the tower and C be the point on the ground. The distance BC = 30 m and the angle of elevation ∠ACB = 30°.
Step 2: In the right-angled triangle ABC, we use the trigonometric ratio: tan θ = Perpendicular / Base. Thus, tan 30° = AB / BC.
Step 3: Substitute the known values into the equation. We know that tan 30° = 1/. So, 1/ = AB / 30.
Step 4: Solve for AB (height of the tower). AB = 30 / . Multiplying numerator and denominator by , we get AB = (30) / 3 = 10 m.