Advertisements
Advertisements
प्रश्न
From the top of a lighthouse, an observer looks at a ship and finds the angle of depression to be 60° . If the height of the lighthouse is 84 meters, then find how far is that ship from the lighthouse? (√3 = 1.73)
उत्तर
As shown in the figure, assume AB as the lighthouse and let A be the position of the observer and C be the position of the ship. Let the distance from the ship to the lighthouse be x.
Let AB be the height of the lighthouse,
∴ AB = 84 metres [Given]
The point 'C' be the position of the ship,
∴ ∠ ACB = 60°
`tan 60° = ("Opposite side of "60°) /("Adjacent side of "60°)`
∴ `tan 60° = "AB" / "BC"`
∴ `sqrt3 = 84/"BC"`
∴ `"BC" = 84/sqrt3`
∴ `"BC" = (84/sqrt3)×sqrt3/sqrt3`
∴ BC = 28√3
∴ BC = 28× 1.73
∴ BC = 48.4 m.
∴ The ship is 48.4 m away from the lighthouse.
APPEARS IN
संबंधित प्रश्न
In the following figure, in ΔABC, BC = 1, AC = 2, ∠B = 90°. Find the value of sin θ.
A man standing on the deck of a ship, which is 10 m above water level, observes the angle of elevation of the top of a hill as 60° and the angle of depression of the base of a hill as 30°. Find the distance of the hill from the ship and the height of the hill
The shadow of a building is 20 m long when the angle of elevation of the sun is 60º. Find the height of the building
The pilot of a helicopter, at an altitude of 1200m finds that the two ships are sailing towards it in the same direction. The angle of depression of the ships as observed from the helicopter are 60º and 45º respectively. Find the distance between the two ships
A tower is 100√3 metres high. Find the angle of elevation of its top from a point 100 metres away from its foot.
From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 20 m high building are 45° and 60° respectively. Find the height of the tower. (Use `sqrt3` = 1.73)
A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is 60°. After some time, the angle of elevation reduces to 30°. Find the distance travelled by the balloon during the interval.
From a point P on the ground the angle of elevation of a 10 m tall building is 30°. A flag is hoisted at the top of the building and the angle of elevation of the top of the flag-staff from P is 45°. Find the length of the flag-staff and the distance of the building from the point P. (Take `sqrt3` = 1.732)
The shadow of a tower standing on a level ground is found to be 40 m longer when Sun’s altitude is 30° than when it was 60°. Find the height of the tower.
From the top of a 50 m high tower, the angles of depression of the top and bottom of a pole are observed to be 45° and 60° respectively. Find the height of the pole.
A tower subtends an angle of 30° at a point on the same level as its foot. At a second point h metres above the first, the depression of the foot of the tower is 60°. The height of the tower is
Find the angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of a tower of height `10sqrt(3)` m
An aeroplane at an altitude of 1800 m finds that two boats are sailing towards it in the same direction. The angles of depression of the boats as observed from the aeroplane are 60° and 30° respectively. Find the distance between the two boats. `(sqrt(3) = 1.732)`
The angle of elevation of a cloud from a point h metres above a lake is β. The angle of depression of its reflection in the lake is 45°. The height of location of the cloud from the lake is
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 B to the West of A?
(sin 55° = 0.8192, cos 55° = 0.5736, sin 42° = 0.6691, cos 42° = 0.7431)
In given figure, the length of AP is ____________.
The angles of elevation of the top of the rock from the top and foot of 100 m high tower are respectively 30° and 45°. The height of the rock is ____________.
An observer 2.25 m tall is 42.75 m away from a chimney. The angle of elevation of the top of the chimney from her eyes is 45°. What is the height of the chimney?
From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are 30° and 45°. If the bridge is at a height of 8 m from the banks, then find the width of the river.
From the top of an 8 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45°. Determine the height of the tower. (Take `sqrt(3)` = 1.732).
