Question

Do the tower. [2016, NCERT EXEMPLAR]
27. From the top of a 7 m high building, the angle of
elevation of the top of a cable tower is 60° and the
angle of depression of its foot is 45°. Determine the
height of the tower
[2018, NCERT EXERCISE]
Com​

Answer 1

Answer:

Given :-

From the top of a 7 m high building, the angle of

elevation of the top of a cable tower is 60° and the

angle of depression of its foot is 45⁰.

To Find :-

Height of tower

Solution :-

For tan 45⁰

Tan = Perpendicular/Base

tan(45) = 7/Base

• tan 45⁰ = 1

1 = 7/Base

1 × Base = 7

Base = 7 m

So, The base are same. Therefore,the base of angle 60⁰ is 7

Now

For tan 60⁰

tan = Perpendicular/Base

tan(60) = Perpendicular/7

• tan 60⁰ = √3

√3 = Perpendicular/7

√3 × 7 = Perpendicular

7√3 = Perpendicular

12.12 = Perpendicular

Now

Height = 12.12 + 7

Height = 19.12 m

Answer 2

Given :-

From the top of a 7 m high building, the angle of

elevation of the top of a cable tower is 60° and the

angle of depression of its foot is 45⁰.

To Find :-

Height of tower

Solution :-

For tan 45⁰

Tan = Perpendicular/Base

tan(45) = 7/Base

tan 45⁰ = 1

1 = 7/Base

1 × Base = 7

Base = 7 m

So, The base are same. Therefore,the base of angle 60⁰ is 7

Now

For tan 60⁰

tan = Perpendicular/Base

tan(60) = Perpendicular/7

tan 60⁰ = √3

√3 = Perpendicular/7

√3 × 7 = Perpendicular

7√3 = Perpendicular

12.12 = Perpendicular

Now

Height = 12.12 + 7

Height = 19.12 m