Advertisements
Advertisements
Question
As observed from the top of a 100 m high lighthouse from the sea-level, the angles of depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships. [Use `sqrt3` = 1.732]
Solution
Let AB be the lighthouse and two ships be at point C and D.
In ΔABC,
tan 45° = `(AB)/(BC)`
⇒ 1 = `100/(BC)`
⇒ BC = 100 m
In ΔABD,
⇒ tan 30° = `(AB)/(BD)`
⇒ `1/sqrt(3) = 100/(100 + CD)`
⇒ 100 + CD = `100sqrt(3)`
⇒ CD = `100(sqrt(3) - 1)`
⇒ CD = 100(1.732 – 1)
⇒ CD = 100 × 0.732
⇒ CD = 73.2 m
Therefore, the distance between the two ships is 73.2 m.
APPEARS IN
RELATED QUESTIONS
At a point A, 20 metres above the level of water in a lake, the angle of elevation of a cloud is 30˚. The angle of depression of the reflection of the cloud in the lake, at A is 60˚.
Find the distance of the cloud from A.
A kit is flying at a height of 75 metres from the ground level, attached to a string inclined at 60 to the horizontal. Find the length of the string to the nearest metre.
From a point on a bridge across a river, the angles of depression of the banks on opposite side of the river are 30° and 45° respectively. If the bridge is at the height of 30 m from the banks, find the width of the river.
From the top of a lighthouse, the angles of depression of two ships on the opposite sides of it are observed to be a and 3. If the height of the lighthouse be h meters and the line joining the ships passes through the foot of the lighthouse, show that the distance
`(h(tan alpha + tan beta))/(tan alpha tan beta)` meters
The angles of elevation of the top of a rock from the top and foot of a 100 m high tower are respectively 30° and 45°. Find the height of the rock.
A tower stands vertically on the ground. From a point on the ground which is 20 m away from the foot of the tower, the angle of elevation of its top is found to be 60°. Find the height of the tower. [Take `sqrt(3)` =1.732 ]
Two men on either side of a 75 m high building and in line with base of building observe the angles of elevation of the top of the building as 30° and 60°. Find the distance between the two men. (Use\[\sqrt{3} = 1 . 73\])
The tops of two poles of height 20 m and 14 m are connected by a wire. If the wire makes an angle of 30° with horizontal, then the length of the wire is
A bird is sitting on the top of a 80 m high tree. From a point on the ground, the angle of elevation of the bird is 45°. The bird flies away horizontally in such away that it remained at a constant height from the ground. After 2 seconds, the angle of elevation of the bird from the same point is 30°. Determine the speed at which the bird flies `(sqrt(3) = 1.732)`
Two towers A and B are standing some distance apart. From the top of tower A, the angle of depression of the foot of tower B is found to be 30°. From the top of tower B, the angle of depression of the foot of tower A is found to be 60°. If the height of tower B is ‘h’ m then the height of tower A in terms of ‘h’ is ____________ m.
