Advertisements
Advertisements
प्रश्न
The angles of depression and elevation of the top of a 12m high building from the top and the bottom of a tower are 60° and 30° respectively. Find the height of the tower, and its distance from the building.
उत्तर
Let AB be the building and CD be the tower.
In ΔABD
`"AB"/"BD" = tan 30^circ`
`12/"BD" = 1/sqrt(3)`
`"BD" = 12sqrt(3)`
In ΔACE
`"AE" = "BD" = 12sqrt(3)`
`"CE"/"AE" = tan 60^circ`
`"CE"/(12sqrt(3)) = sqrt(3)`
`"CE" = 12sqrt(3) xx sqrt(3) = 12 xx 3 = 36`
`"CD" = "CE" + "ED" = 36 + 12 = 48`
So, height of the tower is 48 m and its distance from the building is `12sqrt(3)` m = `12 xx 1.732` m = 20.78 m(approximately)
APPEARS IN
संबंधित प्रश्न
The height of a tree is `sqrt(3)` times the length of its shadow. Find the angle of elevation of the sun.
From the top of a light house 100 m high, the angles of depression of two ships are observed as 48° and 36° respectively. Find the distance between the two ships (in the nearest metre) if:
- the ships are on the same side of the light house,
- the ships are on the opposite sides of the light house.
A man on a cliff observes a boat, at an angle of depression 30°, which is sailing towards the shore to the point immediately beneath him. Three minutes later, the angle of depression of the boat is found to be 60°. Assuming that the boat sails at a uniform speed, determine:
- how much more time it will take to reach the shore?
- the speed of the boat in metre per second, if the height of the cliff is 500 m.
From a window A, 10 m above the ground the angle of elevation of the top C of a tower is x°, where tan `x^circ = 5/2` and the angle of depression of the foot D of the tower is y°, where tan `y^circ = 1/4`. Calculate the height CD of the tower in metres.
A vertical pole is 90m high and the length of its shadow is `90sqrt(3)`. what is the angle of elevation of the sun ?
Due to a heavy storm, a part of a banyan tree broke without separating from the main. The top of the tree touched the ground 15 m from the base making an angle of 45° with the ground. Calculate the height of the tree before it was broken.
An observer, 1.5m tall, is 28.5m away from a tower 30m high. Determine the angle of elevation of the top of the tower from his eye.
Two persons standing on opposite sides of a tower observe the angles of elevation of the top of the tower to be 60° and 50° respectively. Find the distance between them, if the height of the tower is 80m.
From the top of a lighthouse 100 m high the angles of depression of two ships on opposite sides of it are 48° and 36° respectively. Find the distance between the two ships to the nearest metre.
Vertical tower is 20m high. A man standing at some distance from the tower knows that the cosine of the angle of elevation of the top of the tower is 0.53. How far is he standing from the foot of the tower?
