Question

A tower stands vertically on the ground which is 48m away from the foot of the tower angle elevation of th top tower is 30°. Find the height of the tower

Answer 1

The height of the tower is 16√3 m.  

Concept:

• To find height right angle triangle is used.
• The trigonometry formula is used.

Step-by-step explanation:

Step 1: Given conditions are :

Distance between a point on the ground and the foot of a vertical tower, BC = 48 m  

The angle of elevation of the top of the tower, ∠ACB = 30°

Let AB =  'h' m be the height of the tower

In a right-angled triangle, ∆ABC,

$tan C = \frac{AB}{BC}$

tan 30° = $\frac{P}{H}$

$\frac{1}{\sqrt{3}} = \frac{h}{48}$

h = $\frac{48}{\sqrt{3}}$

Step 2: Rationalising the numerator and denominator by √3

$\begin{array}{l}h=(48 \times \sqrt{3}) /(\sqrt{3} \times \sqrt{3}) \\h=(48 \times \sqrt{3}) / 3 \\h=16 \sqrt{3} \mathrm{~m} . \\A B=16 \sqrt{3} \mathrm{~m}\end{array}$

Hence, the height of the tower is 16√3 m.  

Learn more on Brainly:

A tower stand vertically on the ground. From a point on the ground 20 m away from the foot of the tower, the angle of elevation of the top of the tower is 60°. What is the height of the tower?

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From a point on the ground, 20 m away from the foot of a vertical tower, the angle elevation of the top of the tower is 60°, What is the height of the tower?

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Answer 2

The height of the tower would be 16√3m

Given

• 48m away from the foot of the tower
• angle elevation of th top tower is 30°

To find

• height of the tower

solution

we are provided with a tower and the distance between the foot of the tower and the point at which the elevation is made is 48m and the angle of elevation as provided is 30 degree. We are required to estimate the height of the given tower.

kindly refer the attachment for the figure of given condition.

AB represent the height of the tower and BC represents the distance from the foot of the tower to the point which elevation is made .

now,

tan 30 = AB/BC

AB = BC tan30

or, 1/√3 = AB/48

or, AB = 48/√3

rationalising the denominator we get,

AB = (48√3)/3

or, AB = 16√3 m

Therefore, the height of the tower would be 16√3m

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