Advertisements
Advertisements
рдкреНрд░рд╢реНрди
A tower subtends an angle ЁЭЫ╝ at a point A in the plane of its base and the angle if depression of the foot of the tower at a point b metres just above A is β. Prove that the height of the tower is b tan α cot β
рдЙрддреНрддрд░
Let h be the height of tower CD. The tower CD subtends an angle α at a point A. And the angle of depression of foot of tower at a point b meter just above A is β.
Let AC = x and ∠ACB = β, ∠CAD = α
Here we have to prove height of the tower is b tan α cot β
We have the corresponding figure as follows
So we use trigonometric ratios.
In ΔABC
`=> tan beta = (AB)/(AC)`
`=> tan beta = b/x`
`=> x = b/(tan beta)`
`=> x = b cot beta`
Again in ΔACD
`=> tan σ = (CD)/(AC)`
`=> tan alpha = h/x
`=> h = xtan alpha`
`=> h = b tan alpha cot beta`
Hence the height of tower is `b tan alpha cot beta`
APPEARS IN
рд╕рдВрдмрдВрдзрд┐рдд рдкреНрд░рд╢реНтАНрди
A balloon of radius γ makes an angle α at the eye of an observer and the angle of elevation of its centre is β. Then find the height of its centre from the ground level
The horizontal distance between two towers is 60 meters. The angle of depression of the top of the first tower when seen from the top of the second tower is 30° . If the height of the second tower is 90 meters. Find the height of the first tower.
An electrician has to repair an electric fault on a pole of height 4 meters. He needs to reach a point 1 meter below the top of the pole to undertake the repair work. What should be the length of the ladder that he should use, which when inclined at an angle of 60° to the horizontal would enable him to reach the required position?
Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the angels of elevation of the top of the poles are 60° and 30° respectively.
Find the height of the poles and the distances of the point from the poles.
A military tent of height 8.25 m is in the form of a right circular cylinder of base diameter 30 m and height 5.5 m surmounted by a right circular cone of same base radius. Find the length of the canvas used in making the tent, if the breadth of the canvas is 1.5 m.
The top of a 15 m high tower makes an angle of elevation of 60° with the bottom of an electronic pole and angle of elevation of 30° with the top of the pole. What is the height of the electric pole?
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)
The shadow of a tower standing on a level plane is found to be 50 m longer when Sun’s elevation is 30° than when it is 60°. Then the height of the tower is ____________.
A straight highway leads to the foot of a tower. A man standing on the top of the 75 m high tower observes two cars at angles of depression of 30° and 60°, which are approaching the foot of the tower. If one car is exactly behind the other on the same side of the tower, find the distance between the two cars. (use `sqrt(3)` = 1.73)
Read the following passage:
A boy is standing on the top of light house. He observed that boat P and boat Q are approaching the light house from opposite directions. He finds that angle of depression of boat P is 45° and angle of depression of boat Q is 30°. He also knows that height of the light house is 100 m.
|
Based on the above information, answer the following questions.
- What is the measure of ∠APD?
- If ∠YAQ = 30°, then ∠AQD is also 30°, Why?
- Find length of PD
OR
Find length of DQ
