Question

Case study :- 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, including microwave dishes. They are among the tallest human-made structures. There are 2 main types: guyed and self-supporting structures. On a similar concept, a radio station tower was built in two sections A and B. Tower is supported by wires from a point O. Distance between the base of the tower and point O is 36 m. From point O, the angle of elevation of the top of section B is 30° and the angle of elevation of the top of section A is 45°
a. What is the height of the section B ? b. What is the height of the section A ?​

Answer 1

Answer:

(a) height of section B = 20.78 m

(b) height of section A = 36 m

Step-by-step explanation:

Refer to the diagram below

Given, distance between the base of the tower and point O = 36 m

Consider ΔOCB, tan 30 = $\frac{BC}{OC}$

$\frac{1}{\sqrt{3} }= \frac{BC}{36}$

BC = $\frac{36}{\sqrt{3} }$

Hence, BC= 20.78 m

Let 'x' be the height AB

in ΔOAC, tan 45 = $\frac{AB+BC}{OC}$

$1 = \frac{x+20.78}{36}$

Then, 36 = x+ 20.78

Implies, x = 36- 20.78

Hence, x = 15.22 m

Thus,  AC = 15.22+ 20.78 = 36 m

(a) height of section B (BO) = 20.78 m

(b) height of section A (AO) = 36 m

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Answer 2

in ∆Aoc oc=36, find Ac

tan 45 = x/36

1=x/36

x=36 the height of AC = 36

in ∆boc

oc =36 find BC

tan 30=x/36

1/√3 =x/36

=36/√3