Advertisements
Advertisements
Question
From the top of a lighthouse, the angles of depression of two ships on the opposite sides of it are observed to be α, and β. If the height of the light house is 'h' m and the line joining the ships passes through the foot of the light house, show that the distance between the ship is `("h"(tan α + tan β))/(tanα tanβ)`m.
Solution
Let AB be the lighthouse of height h m. Let AC = x and AD = y .
In ΔCAB,
`"AB"/"AC" = tan α`
`tan α = "h"/"x"`
`"x" = "h"/tanα` ....(i)
In ΔDAB,
`"AB"/"AD" = tanβ`
`tanα = "h"/"y"`
`y = "h"/tanβ` ....(ii)
Distance between the ships = x + y
= `"h"/tanα + "h"/tanβ`
= `"h"((tanβ + tanα)/(tanα tanβ))`
APPEARS IN
RELATED QUESTIONS
In the figure given, from the top of a building AB = 60 m high, the angles of depression of the top and bottom of a vertical lamp post CD are observed to 30o and 60o respectively. Find:
1) The horizontal distance between AB and CD.
2) The height of the lamp post.
Two persons are standing on the opposite sides of a tower. They observe the angles of elevation of the top of the tower to be 30° and 38° respectively. Find the distance between them, if the height of the tower is 50 m.
The horizontal distance between two towers is 120 m. The angle of elevation of the top and angle of depression of the bottom of the first tower as observed from the top of the second is 30° and 24° respectively. Find the height of the two towers. Give your answers correct to 3 significant figures.
A vertical pole is 90m high and the length of its shadow is `90sqrt(3)`. what is the angle of elevation of the sun ?
The angle of elevation of the top of an unfinished tower at a point 150 m from its base is 30°. How much higher must the tower be raised so that its angle of elevation at the same point may be 60°?
A 1.4m tall boy stands at a point 50m away from a tower and observes the angle of elevation of the top of the tower to be 60°. Find the height of the tower.
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.
From two points A and B on the same side of a building, the angles of elevation of the top of the building are 30° and 60° respectively. If the height of the building is 10 m, find the distance between A and B correct to two decimal places.
A round balloon of radius 'a' subtends an angle θ at the eye of the observer while the angle of elevation of its centre is Φ. Prove that the height of the centre of the balloon is a sin Φ cosec `θ/2`.
The angle of elevation of a cloud from a point 200 metres above a lake is 30° and the angle of depression of its reflection in the lake is 60°. Find the height of the cloud.
