Question

the angle of elevation of the top of a tower from a point on the ground which is 30m away from the foot of the tower,is 30°. Find the height of the tower

Answer 1

Hey there !

Angle of Elevation = 30°

Distance from the tower = 30 m

Height = ?

We know that tower is perpendicular to the ground. So let us consider the top of tower, the base of the tower and the point of observation to be a right angled triangle.

So we know that,

Tan Ф = Opposite Side / Adjacent Side

According to our assumptions,

Opposite Side = Height of tower

Adjacent Side = Distance from foot of tower

Ф = 30°

=> Tan 30 / Opposite / Adjacent

Let the height be 'h'

=> 1 / √3 = h / 30

-> h = 30 / √3

Rationalising the terms we get,

=> h = 30 × √3 / √3 × √3

=> h = 30√3 / 3

=> h = 10√3 m

We know that √3 = 1.732

=> h = 10 × 1.732 = 17.32 m

Hence the height of the tower is 17.32 m

Hope my answer helped !

Answer 2

Answer:

17.320 m

Step-by-step explanation:

Refer the attached figure

AB = Height of tower

BC = 30 m

∠ACB = 30°

InΔABC

$Tan \theta=\frac{Perpendicular}{Base}$

$Tan30^{\circ}=\frac{AB}{BC}$

$30 \times \frac{1}{\sqrt{3}} = AB$

17.320 = AB

Hence The height of tower is 17.320 m