Maths & Science

What happens if our solar system is just an atom… and the universe is a giant compound made of billions of the same or different atoms?
Then tell me — can we ever find where this universe ends… or is it just the beginning of something much bigger?

Two towers of heights 30 m and 10 m are on a horizontal ground. If the angles of elevation of the top of each tower from the base of the other are complementary, calculate the distance between them.

An aircraft is flying at a vertical height of 100 m above the ground. A person standing on the ground is at a horizontal distance of 100√3 m from the point directly below the aircraft. Determine the angle of elevation of the aircraft from the person’s position.

Solve 2x + 3y = 11 and 2x – 4y = – 24 and hence find the value of ‘m’ for which y = mx + 3.

Find the coordinates of the point which divides the line joining (–1, 7) and (4, –3) in the ratio 2 : 3.

Doppler Effect

Gravity

A man at the top of a tower observes a car moving towards him. The angle of depression changes from 30° to 45° in 10 minutes. How long will the car take to reach the base after the angle becomes 45°?

From the base of a building, the angle of elevation of the top of a tower is 45°. From the top of the building, it is 30°. If a person moves 9 m towards the tower and observes the angle as 60°, find the height of the building.

Expand the expression:

Algebraic solution

Two vertical structures, 14 m and 9 m in height, stand apart. The angles of elevation of their tops from each other's bases add up to 90°. Find the distance between them.