Advertisements
Advertisements
Question
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.
Solution
Let AC and BD be the two poles of the same height h m.
Given AB = 80 m
Let, AP = x m, therefore, PB = (80 − x) m
In triangles APC and BPD
`tan 30^@((AC)/(AP))=h/x` and `tan60^@((BD)/(AB))=H/(80-x)`
`therefore(tan30^@)/(tan60^@)=x/(h/(80-x))=(80-x)/x`
`rArr1/3=(80-x)/xrArr=60m`
`thereforeh=xtan30^@` `60/sqrt3=20sqrt3m.`
Therefore, the height of the poles is `20sqrt3`and the distances of the point from the poles are 60 m and 20 m.
APPEARS IN
RELATED QUESTIONS
A bucket open at the top is in the form of a frustum of a cone with a capacity of 12308.8 cm3. The radii of the top and bottom circular ends are 20 cm and 12 cm, respectively. Find the height of the bucket and the area of metal sheet used in making the bucket. (use π = 3.14)
A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is 60°. After some time, the angle of elevation reduces to 30°. Find the distance travelled by the balloon during the interval.
The length of a string between a kite and a point on the ground is 90 meters. If the string makes an angle O with the ground level such that tan O = 15/8, how high is the kite? Assume that there is no slack in the string.
From the top of a tower of height 50 m, the angles of depression of the top and bottom of a pole are 30° and 45° respectively. Find
(i) how far the pole is from the bottom of a tower,
(ii) the height of the pole. (Use \[\sqrt{3} = 1 . 732\])
A bucket is in the form of a frustum of a cone and it can hold 28.49 litres of water. If the radii of its circular ends are 28 cm and 21 cm, find the height of the bucket. [Use`pi22/7` ]
The angle of elevation of a cloud from a point h metre above a lake is θ. The angle of depression of its reflection in the lake is 45°. The height of the cloud is
At some time of the day, the length of the shadow of a tower is equal to its height. Then, the sun’s altitude at that time is ______.
An observer `sqrt3` m tall is 3 m away from the pole `2 sqrt3` high. What is the angle of elevation of the top?
The angles of depression of the top and the bottom of a 10 m tall building from the top of a multi-storeyed building are 30° and 45°, respectively. Find the height of the multi-storeyed building.
The angles of elevation of the bottom and the top of a flag fixed at the top of a 25 m high building are 30° and 60° respectively from a point on the ground. Find the height of the flag.
