**Q) Radio towers are used for transmitting a range of communication services including radio and television. The tower will either act as an antenna itself or support one or more antennas on its structure.**

**On a similar concept, a radio station tower was built in two stations A and B (B vertically below A). The tower is supported by wires AO and BO from a point O on the ground. Distance between the base C of the tower and the point O is 36 m. From O, the angles of elevation of the tops of station B and station A are 30º and 45º respectively.**

**Based on the above, answer the following questions :**

**(i) Find the height of station B. **

**(ii) Find the height of station A. **

**(iii) (a) Find the length of the wire OA. **

**OR**

**(iii) (b) Find the length of the wire OB.**

**An**s:

**STEP BY STEP SOLUTION**

First, we make a diagram for the question.

**(i) Height of station B:**

Let’s start from Δ BOC:

tan ∠ BOC =

∴

∴

∴

∴ X = 12 √3

**Therefore, the height of tower B is 12 √3 m.**

**(ii) Height of station A:**

In Δ AOC:

tan ∠ AOC =

∴

∴ 1 =

∴ H = 36

**Therefore, the height of tower A is 36 m.**

**(iii) (a) Length of wire OA:**

In Δ AOC:

cos ∠ AOC =

∴

∴

∴ OA = 36 √2

**Therefore, the length of wire OA is 36 √2 m.**

**(iii) (b) Length of wire OB:**

In Δ BOC:

cos ∠ BOC =

∴

∴

∴ OB =

∴ OB = 24 √3

**Therefore, the length of wire OA is 24 √3 m.**

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