Q) From a point on the ground, the angles of elevation of the bottom and top of a transmission tower fixed at the top of 20m high building are 45⁰ and 60⁰ respectively. Find the height of the transmission tower.

Ans:

Step 1: Let’s start by drawing a diagram for this question:

Here, we can see AB is 20 m high building and PA is the tower on top of building. Angle from Point C to point A is 45⁰ and to Point P is 60⁰. We need to find height H of tower PA.

Step 2:

Let’s start from Δ ABC, here tan C =

∴ tan 45 =

∴ 1 =

∴ D = 20 m

Step 3:

Next, Let’s take in Δ PBC, here tan C =

∴ tan 60 =

∴

∴ 20√3 = 20 + H

∴ H = 20√3 – 20 = 20(√3 – 1) = 20 x 0.732 = 14.64m

Therefore, the height of the transmission tower is 20(√3 – 1)m or 14.64m
Note: calculate value in decimal terms, only if it is given that √3 = 1.732 in the question.

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