If a pole of 54m height casts a shadow of 18`sqrt(3)` m long on the ground. Then the Sun’s angle of elevation at that instant is

In ∆ ABC tanθ= AB/BC = 54/(18√3) tanθ= 3/√3 = √3 tanθ= tan(60˚) θ = 60˚

- 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.
- Find the area of maximum side of square that can be inscribed in a right angled triangle of side 15, 20 and 25 cm.
- A boat is being rowed away from a cliff 240 m high. From the top of the cliff, the angle of depression of the boat changes from 60° to 45° in 3 minutes. What is the speed of the boat?
- 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)
- 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.
- A pole 9√3m high casts a shadow 27 m long on the ground. Find the angle of elevation
- 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 distance between two parallel poles is 65√3 m. The angle of depression of the top of the second pole when seen from the top of first pole is 30
^{o }. What will be the height of second pole if the first pole is 110 m long? - 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?
- A boat is being rowed away from a cliff 270 m high. From the top of the cliff, the angle of depression of the boat changes from 60° to 45° in 2 minutes. What is the speed of the boat?

More Height and Distance Questions

×