Advertisements
Advertisements
प्रश्न
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.
उत्तर
Two persons A and B are standing on the opposite side of the tower TR and height of tower TR = 50 m and angles of elevation with A and B are 30° and 38° respectively.
Let AR = x and RB = y
Now in right ΔTAR, we have
`tan theta = (TR)/(AR)`
`=> tan 30^circ = 50/x`
`=> 1/sqrt(3) = 50/x `
∴ `x = 50sqrt(3) = 86.60 m`
Again in right ΔTRB, we have
`tan 38^circ = 50/y`
`=>` y tan 38° = 50
`y = 50/tan 38^circ`
= `50/0.7813`
= 63.99
or 64.00 m ...(i)
∴ Distance between A and B
= x + y
= 86.60 + 64.00
= 150.6 m
APPEARS IN
संबंधित 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
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.
A man standing on the bank of a river observes that the angle of elevation of a tree on the opposite bank is 60°. When he moves 50 m away from the bank, he finds the angle of elevation to be 30°.
Calculate :
- the width of the river;
- the height of the tree.
The angle of elevation of the top of a vertical cliff from a point 30 m away from the foot of the cliff is 60°. Find the height of the cliff.
Find the angle of depression from the top of a 140m high pillar of a milestone on the ground at a distance of 200m from the foot of the pillar.
The height of an observation tower is 180m above sea level. A ship coming towards the tower is observed at an angle of depression of 30°. Calculate the distance of the boat from the foot of the observation tower.
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.
A man on the deck of a ship is 10 m above the water level. He observes that the angle of elevation of the top of a diff is 45° and the angle of depression of the base is 30°. Find the distance of the diff from the ship and the height of the cliff.
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 shadow of a vertical tower on a level ground increases by 10 m when the altitude of the sun changes from 45° to 30°. Find the height of the tower, correct to two decimal places.
