Question

A TV tower stands vertically on the side of a road. From a point on the other side directly opposite to the tower, the angle of elevation of the top of tower is 60°. From another point 10 m away from this point, on the line joining this
point to the foot of the tower, the angle of elevation of the top of the tower is 30°. Find the height of the tower and the width of the road.
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Answer 1

QUESTION :-

A TV tower stands vertically on the side of a road. From a point on the other side directly opposite to the tower, the angle of elevation of the top of tower is 60°. From another point 10 m away from this point, on the line joining this point to the foot of the tower, the angle of elevation of the top of the tower is 30°. Find the height of the tower and the width of the road.

SOLUTION :-

Let h mts be the height of the tower

x m be the width of the road

Distance between 2 points of observation = 10 cm

Angles of elevation from the 2 points = 60° & 30°.

Refer the image

From the figure

tan60° = h/x

➡ √3 = h/x

➡ h = √3x .............( 1 )

Also tan30° = h/10+x

➡ 1/√3 = h/10 + x

➡ h = 10+x/√3 ...........( 2 )

From equation 1 and 1

h = √3x = 10+x/√3

.°. √3 x = 10+x/√3

➡ √3.√3x = 10 + x

➡ 3x - x = 10

➡ 2x = 10

➡ x = 10/2

➡ x = 5

.°. Width of the road = 5 m

Height of the tower = √3x = 5√3 m

Answer 2

Let,

h mts be the height

Distance between 2points = 10cm

Angles of elevation = 60° and 30°

Fr the figure

Tan60° = h/x

$\sqrt{3} \frac{h}{x}$

h=√3x

h=√3x=10+x/√3

√3×√3=10+x

3x-x=10

2x=10

x=10/2

X=5m

And

Height = √3x=5√3 m