Advertisements
Advertisements
प्रश्न
From a point on the ground 40m away from the foot of a tower, the angle of elevation of the top of the tower is 30 . The angle of elevation of the top of a water tank (on the top of the tower) is 45 , Find (i) the height of the tower, (ii) the depth of the tank.
उत्तर
Let BC be the tower and CD be the water tank.
We have,
AB = 40m, ∠BAC = 30° and ∠BAD = 45°
In ΔABD,
` tan 45° = (BD)/(AB)`
`⇒ 1 = (BD)/40`
⇒ BD = 40 M
Now, in Δ ABC
`tan 30° = (BC)/(AB)`
`⇒1/ sqrt(3) = (BC) /40`
`⇒ BC = 40/sqrt(3)`
`⇒ BC = 40/ sqrt(3) xx sqrt(3)/sqrt(3)`
`⇒ BC = (40sqrt(3) )/3 m`
`"(i) The height of the tower," BC = (40 sqrt(3))/3 = (40 xx 1.73)/3 = 23.067 ~~ 23.1 m`
`"(ii) The depth of the tank " CD = (BD - BC) = (40-23.1 ) = 16.9 m`
APPEARS IN
संबंधित प्रश्न
A boat is being rowed away from a cliff 150m high. At the top of the cliff the angle of depression of the boat changes from 60º to 45º in 2 minutes. Find the speed of the boat.
Two poles of equal heights are standing opposite each other an either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60° and 30º, respectively. Find the height of poles and the distance of the point from the poles.
A pole casts a shadow of length \[2\sqrt{3}\] m on the ground, when the sun's elevation is 60°. Find the height of the pole.
A ladder on the platform of a fire brigade van can be elevated at an angle of 70° to the maximum. The length of the ladder can be extended upto 20 m. If the platform is 2m above the ground, find the maximum height from the ground upto which the ladder can reach. (sin 70° = 0.94)
From the top of the tower 60 m high the angles of depression of the top and bottom of a vertical lamp post are observed to be 38° and 60° respectively. Find the height of the lamp post (tan 38° = 0.7813, `sqrt(3)` = 1.732)
If the angle of elevation of a cloud from a point ‘h’ metres above a lake is θ1 and the angle of depression of its reflection in the lake is θ2. Prove that the height that the cloud is located from the ground is `("h"(tan theta_1 + tan theta_2))/(tan theta_2 - tan theta_1)`
Three villagers A, B and C can see each other using telescope across a valley. The horizontal distance between A and B is 8 km and the horizontal distance between B and C is 12 km. The angle of depression of B from A is 20° and the angle of elevation of C from B is 30°. Calculate the vertical height between A and B. (tan 20° = 0.3640, `sqrt3` = 1.732)
The electric pole subtends an angle of 30° at a point on the same level as its foot. At a second point ‘b’ metres above the first, the depression of the foot of the pole is 60°. The height of the pole (in metres) is equal to
A bird is flying from A towards B at an angle of 35°, a point 30 km away from A. At B it changes its course of flight and heads towards C on a bearing of 48° and distance 32 km away. How far is C to the North of B?
(sin 55° = 0.8192, cos 55° = 0.5736, sin 42° = 0.6691, cos 42° = 0.7431)
The angles of elevation of the top of a tower from two points distant s and t from its foot are complementary. Then the height of the tower is ____________.
