Home
Class 12
MATHS
PQR is a triangular park with PQ=PR=200m...

PQR is a triangular park with PQ=PR=200m . A T.V tower stands at the mid-point of QR. If the angles of elevation of the top of the tower at P , Q and R respectively `45^@` , `30^@` and `30^@` then the height of the tower in m is

A

100

B

50

C

`100 sqrt(3)`

D

`50 sqrt(2)`

Text Solution

Verified by Experts

The correct Answer is:
A

Let height of tower TM be h.
In `DeltaPMT, tan 45^(@) = (TM)/(PM)`
`implies 1=(h)/(PM)`
implies PM=h
In `DeltaTQM, tan 30^(@) = (h)/(QM), QM=sqrt(3)h`
In `DeltaPMQ, PM^(2)+QM^(2)=PQ^(2)`
`h^(2)+(sqrt(3)h)^(2)=(200)^(2)`
`implies 4h^(2)=(200)^(2)`
`implies h = 100m`
Promotional Banner

Similar Questions

Explore conceptually related problems

If the angle of elevation of the top of a tower at a distance 500 metres from its foot is 30^@ then the height of the tower is

ABC is a triangular park with AB = AC = 100 m. A vertical tower is situated at the mid-point of BC. If the angles of elevation of the top of the tower at A and B are cot^(-1)(3sqrt(2)) and cosec^(-1)(2sqrt(2)) respectively, then the height of the tower (in m) is

the angle of elevation of the top of a tower at a point on the ground 50m away from the foot of the tower is 45^(@) . Then the height of the tower ( in meters ) is ………. .

From the top of a 12 m high building, the angle of elevation of the top of a cable tower is 60^(@) and the angle of depression of its foot is 30^(@) . Determine the height of the tower .

The angle of elevation of the top of a hill at a point on the ground 130 m away from the foot of the tower is 45^(@) . Then the height of the tower ( in meter ) is .........

Find the angle of elevation of the top of a tower from a point on the ground, which is 30 m away the foot of a tower of height 10sqrt(3) m.

A tower stands vertically on the ground. From a point which is 15 meter away from the foot of the tower, the angle of elevation of the top of the tower is 45^(@) . What is the height of the tower?