What is the distance between the top of a 30 feet high tower and the tip of its 40 feet long shadow which theorem you should use for calculating this question?

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Solution:

Given, the angle of elevation of the top of a tower 30 m high from the foot of another tower in the same plane is 60°

The angle of elevation of the top of the second tower from the foot of the first tower is 30°

We have to find the distance between the two towers and also the height of the other tower.

Let BQ be the first tower with height 30 m

Angle of elevation, ∠QAB = 60°

Let PA be the second tower with height h m

Angle of elevation, ∠PBA = 30°

AB is the distance between the two towers.

In triangle AQB,

By pythagorean theorem,

tan 60° = QB/AB

By trigonometric ratio of angles,

tan 60° = √3

So, √3 = 30/AB

AB = 30/√3 m

AB = 3(10)/√3

AB = 10√3 m

Therefore, the distance between two towers is 10√3 m.

In triangle APB,

By using pythagorean theorem,

tan 30° = AP/AB

By trigonometric ratio of angles,

tan 30° = 1/√3

So, 1/√3 = AP/(30/√3)

AP = (30/√3)/√3

AP = 30/3

AP = 10 m

Therefore, the height of the second tower is 10 m.

✦ Try This: The angle of elevation of the top of a cell phone tower from the foot of a high apartment is 60° and the angle of depression of the foot of the tower from the top of the apartment is 30°. If the height of the apartment is 50 m, find the height of the cell phone tower. According to radiations control norms, the minimum height of a cell phone tower should be 120 m. State if the height of the above mentioned cell phone tower meets the radiation norms.

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 8

NCERT Exemplar Class 10 Maths Exercise 8.4 Problem 13

Summary:

The angle of elevation of the top of a tower 30 m high from the foot of another tower in the same plane is 60° and the angle of elevation of the top of the second tower from the foot of the first tower is 30°. The distance between the two towers is 10√3 m and also the height of the other tower is 10 m

☛ Related Questions:

The angle of elevation of the top of a tower 30m high from the foot of another tower in the same plane is 60∘ and the angle of elevation of the top of the second tower from the foot of the first tower is 30∘. Find the distance between the two towers and also the height of the tower.

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