Advertisements
Advertisements
Question
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)
Solution
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
RELATED QUESTIONS
The angle of elevation of the top of a hill at the foot of a tower is 60° and the angle of elevation of the top of the tower from the foot of the hill is 30°. If height of the tower is 50 m, find the height of the hill.
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 tower stands vertically on the ground. From a point on the ground, 20 m away from the foot of the tower, the angle of elevation of the top of the tower is 600. What is the height of the tower?
A vertically straight tree, 15 m high, is broken by the wind in such a way that its top just touches the ground and makes an angle of 60° with the ground. At what height from the ground did the tree break?
From a point on a bridge across a river, the angles of depression of the banks on opposite side of the river are 30° and 45° respectively. If the bridge is at the height of 30 m from the banks, find the width of the river.
Two buildings are in front of each other on a road of width 15 meters. From the top of the first building, having a height of 12 meter, the angle of elevation of the top of the second building is 30°.What is the height of the second building?
The angle of depression of the top and bottom of 20 m tall building from the top of a multistoried building are 30° and 60° respectively. The height of the multistoried building and the distance between two buildings (in metres) is
If at some time, the length of the shadow of a tower is `sqrt3` times its height, then the angle of elevation of the sun, at that time is ____________.
In figure given ABCD is a rectangle, the value of CE is ____________.
A Technician has to repair light on a pole of height 10 m. She needs to reach a point 1 m below the top of the pole to undertake the repair work. What should be the length of the ladder that she should use which, when inclined at an angle of 60∘ to the ground, would enable her to reach the required position? Also, how far from the foot of the pole should she place the foot of the ladder?
