From the top of a tower of height 40 feet, the angles of depression of two objects south and north of the tower are both 45°. What is the distance between the two objects (in feet)?

In ΔABC, tan 45° = 40/CB ⇒ 1 = 40/CB ⇒ CB = 40 feet In ΔABD, tan 45° = 40/BD ⇒ 1 = 40/BD ⇒ BD = 40 feet CD = CB + BD = 40 + 40 = 80 feet

- There are two houses of the same height on both sides of a 15-meter wide road. From a point on the road, elevation angles of the houses are 30° and 60° respectively. Find the height of the houses.
- At the foot of the Lighthouse, the elevation of its top is 45⁰. A Bird after flying 8 km towards the building up a slope of 30⁰ inclinations, the elevation is found to be 60⁰. Then find the height of the Lighthouse.
- There is a 12 m tall hoarding pole on the top of a building. A person at some distance from the building, observes that the angle of elevation to the top of the hoarding pole from that point is the same as the angle of elevation to the bottom of the hoarding pole if he moves 4 √ 3 m closer to the building. What is the angle of elevation that the person is seeing?
- 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?
- The height of a conical tent is 9m. A vertical pole of 6m height is placed 4 m away from its centre such that it touches the surface. Find the slant height of the tent from the base to the point where the pole touches it?
- A pole got broken by the wind whose top meets the ground at an angle of 30° at a distance of 45 meters from the foot. What was the total height of the pole?
- From 110m high towers, the angle of depression of a car is 45°. Then how far the car is from 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.
- From the top of a lighthouse, the angle of depression to the top and bottom of a tower is 30° and 45°, respectively. If the lighthouse is 210 metres high, then find the height of the tower.

More Height and Distance Questions

×