Advertisements
Advertisements
प्रश्न
The angle of elevation from a point P of the top of a tower QR, 50 m high is 60o and that of the tower PT from a point Q is 30°. Find the height of the tower PT, correct to the nearest metre
उत्तर
In ΔPQR
`tan 60^@ = (RQ)/(PQ)`
`sqrt3 = 50/(PQ)`
`PQ = 50/sqrt3`
In ΔPQT
`tan 30^@ = (PT)/(PQ)`
`1/sqrt3 = (PT)/(50/sqrt3)`
`PT = 1/sqrt3 xx 50/sqrt3 = 50/3`
APPEARS IN
संबंधित प्रश्न
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.
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.
Find the length of the shadow cast by a tree 60 m high when the sun's altitude is `30^circ`.
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.
An aeroplane at an altitude of 200 m observes the angles of depression of opposite points on the two banks of a river to be 45° and 60°. Find the width of the river.
An aeroplane when flying at a height of 4km from the ground passes vertically above another aeroplane at an instant when the angles of the elevation of the two planes from the same point on the ground are 60° and 45° respectively. Find the vertical distance between the aeroplanes at that instant.
The angle of elevation of a stationary cloud from a point 25m above a lake is 30° and the angle of depression of its reflection in the lake is 60°. What is the height of the cloud above the lake-level?
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.
Two men on either side of a temple 75 m high observed the angle of elevation of the top of the temple to be 30° and 60° respectively. Find the distance between the two men.
An aeroplane when 3,000 meters high passes vertically above another aeroplane at an instance when their angles of elevation at the same observation point are 60° and 45° respectively. How many meters higher is the one than the other?
