Advertisements
Advertisements
प्रश्न
Three villagers A, B and C can see each other using telescope across a valley. The horizontal distance between A and B is 8 km and the horizontal distance between B and C is 12 km. The angle of depression of B from A is 20° and the angle of elevation of C from B is 30°. Calculate the vertical height between B and C. (tan 20° = 0.3640, `sqrt3` = 1.732)
उत्तर
Let AD is the vertical height between A and B
In the right ∆ABD
tan 20° = `"AD"/"BD"`
0.3640 = `"AD"/8`
AD = 0.3640 × 8 = 2.912 km
∴ AD = 2.91 km
CE is the vertical height between C and B
In the right ∆BCE, tan 30° = `"CE"/"BE"`
`1/sqrt(3) = "CE"/12`
⇒ `sqrt(3)"CE"` = 12
CE = `12/sqrt(3)`
= `(12 xx sqrt(3))/(sqrt(3) xx sqrt(3))`
= `(12 xx sqrt(3))/3`
= `4sqrt(3)`
= 4 × 1.732
= 6.928
= 6.93 km
The vertical height between B and C = 6.93 km
APPEARS IN
संबंधित प्रश्न
The heights of two poles are 80 m and 62.5 m. If the line joining their tops makes an angle of 45º with the horizontal, then find the distance between the pole
An aeroplane is flying at a height of 300 m above the ground. Flying at this height, the angles of depression from the aeroplane of two points on both banks of a river in opposite directions are 45° and 60° respectively. Find the width of the river. [Use `sqrt3` = 1⋅732]
A 1.6 m tall girl stands at a distance of 3.2 m from a lamp-post and casts a shadow of 4.8 m on the ground. Find the height of the lamp-post by using (i) trigonometric ratios (ii) property of similar triangles.
A tree breaks due to the storm and the broken part bends so that the top of the tree touches the ground making an angle of 30° with the ground. The distance from the foot of the tree to the point where the top touches the ground is 10 metres. Find the height of the tree.
A ladder rests against a wall at an angle α to the horizontal. Its foot is pulled away from the wall through a distance a so that it slides a distance b down the wall making an angle β with the horizontal. Show that `a/b = (cos alpha - cos beta)/(sin beta - sin alpha)`
The vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height 6m. At a point on the plane, the angle of elevation of the bottom of the flagstaff is
30 and that of the top of the flagstaff 60 . Find the height of the tower
[Use `sqrt(3)` 1.732 ]
A man on the deck of a ship, 16m above water level, observe that that angle of elevation and depression respectively of the top and bottom of a cliff are 60° and 30° . Calculate the distance of the cliff from the ship and height of the cliff.
From the top of a lighthouse, the angle of depression of two ships on the opposite sides of it is observed to be 30° and 60°. If the height of the lighthouse is h meters and the line joining the ships passes through the foot of the lighthouse, show that the distance between the ships is `(4"h")/sqrt(3)` m
If the length of the shadow of a tower is increasing, then the angle of elevation of the sun ____________.
From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are 30° and 45° respectively. If the bridge is at a height of 3 m from the banks, find the width of the river. (Use `sqrt(3)` = 1.73)
