Advertisements
Advertisements
Question
The angles of elevation of the top of a tower from two points at distance of 5 metres and 20 metres from the base of the tower and is the same straight line with it, are complementary. Find the height of the tower.
Solution
Let the height of the tower be AB.
We have.
AC = 5m, AD = 20m
Let the angle of elevation of the top of the tower (i.e. ∠ACB) from point C be θ .
Then,
the angle of elevation of the top of the tower (i.e. Z ADB) from point D
=(90° -θ)
Now, in ΔABC
`tan theta = (AB)/(AC)`
`⇒ tan theta = (AB)/5` ...................(i)
Also, in ΔABD,
`cot (90° - theta ) = (AD)/(AB)`
`⇒ tan theta = 20/(AB)` .................(ii)
From (i) and (ii), we get
`(AB)/5 = 20/(AB)`
`⇒ AB^2 = 100`
`⇒ AB = sqrt(100)`
∴ AB = 10 m
So, the height of the tower is 10 m.
APPEARS IN
RELATED QUESTIONS
There is a small island in the middle of a 100 m wide river and a tall tree stands on the island. P and Q are points directly opposite to each other on two banks, and in line with the tree. If the angles of elevation of the top of the tree from P and Q are respectively 30º and 45º, find the height of the tree. (Use `sqrt(3)` = 1.732)
A tree is broken by the wind. The top of that tree struck the ground at an angle of 30° and at a distance of 30. Find the height of the whole tree
The angle of elevation of the top of a tower as observed form a point in a horizontal plane through the foot of the tower is 32°. When the observer moves towards the tower a distance of 100 m, he finds the angle of elevation of the top to be 63°. Find the height of the tower and the distance of the first position from the tower. [Take tan 32° = 0.6248 and tan 63° = 1.9626]
From the point of a tower 100m high, a man observe two cars on the opposite sides to the tower with angles of depression 30° and 45 respectively. Find the distance between the cars
A storm broke a tree and the treetop rested 20 m from the base of the tree, making an angle of 60° with the horizontal. Find the height of the tree.
Two poles are 25 m and 15 m high, and the line joining their tops makes an angle of 45° with the horizontal. The distance between these poles is ______.
An observer 1.5 m tall is 28.5 m away from a tower. The angle of elevation of the top of the tower from her eyes is 45°. What is the height of the tower?
Two towers A and B are standing some distance apart. From the top of tower A, the angle of depression of the foot of tower B is found to be 30°. From the top of tower B, the angle of depression of the foot of tower A is found to be 60°. If the height of tower B is ‘h’ m then the height of tower A in terms of ‘h’ is ____________ m.
A ladder 15 meters long just reaches the top of a vertical wall. If the ladder makes an angle of 60° with the wall, then the height of the wall will be ____________.
A window of a house is h metres above the ground. From the window, the angles of elevation and depression of the top and the bottom of another house situated on the opposite side of the lane are found to be α and β, respectively. Prove that the height of the other house is h(1+ tan α tan β) metres.
