Question

a man observes the angle of elevation of the top of the tower to be 45 degree he walks towards it in horizontal line through its base on covering 20 m the angle of elevation changes to 60 degree find the height of the tower correct to two significant figures

Answer 1

Hello Friend...☺

Using trignometric ratios:

tan60 = Height/base

tan45 = Height/20+base

$\tan(60) = \sqrt{3} \\ \tan(45) = 1$

$height = base \times \sqrt{3} \\ height = 20 + base$

Soloving equations simultaneosly:

Height = 47.32 m

Heope this helps you...❤

Answer 2

Answer:

Step-by-step explanation:

We will trigonometric ratios in this question.

Here we have two right angled triangles with a common height.

One has the following properties.

Adjacent angle = 45° and height h

The other one has adjacent angle = 60° and height h.

Let the remaining distance to the base of the tower be x.

The total distance to the base of the tower from the point the man began will be :

(x + 20) cm

At angle of elevation 45° :

Base = (x + 20)cm

h = height

h = (x + 20) / Tan 45°

At angle of elevation 60°:

Base = x cm

h = height

h = xTan 60°

Equating the two we have :

(x + 20)Tan 45 = xTan 60

Tan 45 = 1

Tan 60 = √3

Doing the substitution we have :

x + 20 = x√3

x + 20 = x√3

x + 20 = 1.7321x

1.7321x - x = 20

0.7321x = 20

x = 27.32 m

height = 27.32 + 20 = 47.32 m

= 47.32 m