Advertisements
Advertisements
प्रश्न
A vertical pole and a vertical tower are on the same level ground in such a way that from the top of the pole, the angle of elevation of the top of the tower is 60o and the angle of depression of the bottom of the tower is 30o. Find: the height of the pole, if the height of the tower is 75 m.
उत्तर
Let AB be the tower and CD be the pole.
Then ∠ ACE = 60° and ∠ BCE = 30°
Let height of the pole be x m
∴ CD=Be=x
In Δ BEC,
`(BE)/(EC)=tan 30° `
⇒ `EC=sqrt3 x`
`In Δ (AE)/(EC)=tan 60°`
`⇒ (75-x)/(EC)= sqrt3`
⇒ 75-x=3x
`∴ x=75/4=18.75 m`
∴ height of the pole is 18.75m.
APPEARS IN
संबंधित प्रश्न
Evaluate without using trigonometric tables.
`2((tan 35^@)/(cot 55^@))^2 + ((cot 55^@)/(tan 35^@)) - 3((sec 40^@)/(cosec 50^@))`
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.
A boy, 1.6 m tall, is 20 m away from a tower and observes the angle of elevation of the top of the tower to be (i) 45°, (ii) 60°. Find the height of the tower in each case.
The upper part of a tree, broken over by the wind, makes an angle of 45° with the ground and the distance from the root to the point where the top of the tree touches the ground is 15 m. What was the height of the tree before it was broken?
In the figure, given below, it is given that AB is perpandiculer to BD and is of length X metres. DC = 30 m, ∠ADB = 30° and ∠ACB = 45°. Without using tables, find X.
Find AD.
A flagstaff stands on a vertical pole. The angles of elevation of the top and the bottom of the flagstaff from a point on the ground are found to be 60° and 30° respectively. If the height of the pole is 2.5m. Find the height of the flagstaff.
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.
The angle of elevation of the top Q of a vertical tower PQ from a point X on the ground is 60°. At a point Y, 40m vertically above X, the angle of elevation is 45°. Find the height of the tower PQ and the distance XQ.
The angle of elevation of the top of a 100 m high tree from two points A and B on the opposite side of the tree are 52° and 45° respectively. Find the distance AB, to the nearest metre.
