The angle of depression of a point on the ground as seen from the top of a tower, 65 feet high, is 45°. Find the distance of the point on the ground from the foot of the tower.

Let θ be the angle of depression of the point on the ground as seen from the top of a tower, here θ = 45° Let AC be the height of the tower, here AC = 65 feet. Let the distance of the point on the ground from the foot of the tower, AB = x feet. Here, tan θ = AC/AB ⇒ tan 45° = 65/x ⇒ 1 = 65/x ⇒ x = 65 feet

- Two men are on opposite sides of a tower of 75 m height. If they measure the elevation of the top of the tower as 30deg; and 45deg; respectively then the distance between the men is?

- The shadow of a pole 24m long is 56m. Then what will be the approximate shadow of building 40m high at the similar situation?
- A pole 9√3m high casts a shadow 27 m long on the ground. Find the angle of elevation
- A tree breaks due to storm and the broken part bends, so that the top of the tree touches the ground making an angle of 30° with the ground. The distance between the foot of the tree to the point where the top touches the ground is 12 m. Find the height of the tree (in metres)
- A Navy captain going away from a lighthouse at the speed of 4[(√3) – 1] m/s. He observes that it takes him 1 minute to change the angle of elevation of the top of the lighthouse from 60o to 45o. What is the height (in metres) of the lighthouse?
- The length of the shadow of a vertical tower increases by 9 m on horizontal ground when the height of the sun changes from 45° to 30 ° , then find the height of the tower?
- Two boys are on opposite sides of a tower of 100 m height. If they measure the elevation of the top of the tower as 30° and 45° respectively then the distance between the boys is?
- A man 2 m tall is 25 m away from a tower 27 m high. Determine the angle of elevation of the top of the tower from the eye of the observer.
- The angle of elevation of the top of a building from the foot of a tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the height of the tower is 18 m, what is the height of the building?
- Two buildings are collinear with the base of a tower and are at a distance 9m and 16m from the base of the tower. The angles of elevation from these two building of the top of the tower are complementary. What is the height of the tower?

More Height and Distance Questions

×