Advertisements
Advertisements
प्रश्न
The angle of elevation on the top of a building from the foot of a tower is 30° . The angle of elevation of the top of the tower when seen from the top of the second water is 60° .If the tower is 60m high, find the height of the building.
उत्तर
Let AB be thee building and PQ be the tower.
We have,
PQ = 60m,∠APB = 30°, ∠PAQ = 60°
In ΔAPQ,
` tan 60° = (PQ)/(AP)`
`⇒ sqrt(3) = 60/(AP)`
`⇒ AP = 60/sqrt(3)`
`⇒ AP = (60 sqrt(3))/3`
`⇒ AP = 20 sqrt(3) m`
Now , in Δ ABP ,
` tan 30° = (AB)/(AP)`
`⇒1/ sqrt(3) = (AB)/(20 sqrt(3))`
`⇒ AB = (20 sqrt(3))/ sqrt(3)`
∴ AB = 20 m
So, the height of the building is 20 m
APPEARS IN
संबंधित प्रश्न
A ladder of length 6meters makes an angle of 45° with the floor while leaning against one wall of a room. If the fort of the ladder is kept fixed on the floor and it is made to lean against the opposite wall of the room, it makes an angle of 60° with the floor. Find the
distance between two walls of the room.
A person is standing at a distance of 80 m from a church looking at its top. The angle of elevation is of 45°. Find the height of the church.
From a point on the ground, 20 m away from the foot of a vertical tower, the angle elevation of the top of the tower is 60°, What is the height of the tower?
An aeroplane at an altitude of 1800 m finds that two boats are sailing towards it in the same direction. The angles of depression of the boats as observed from the aeroplane are 60° and 30° respectively. Find the distance between the two boats. `(sqrt(3) = 1.732)`
The line drawn from the eye of an observer to the point in the object viewed by the observer is known as ____________.
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?
The angle of elevation of the top of a vertical tower from a point on the ground is 60°. From another point, 10 m vertically above the first, its angle of elevation is 45°. Find the height of the tower.
If one looks from a tower 10 m high at the top of a flag staff, the depression angle of 30° is made. Also, looking at the bottom of the staff from the tower, the angle of the depression made is of 60°. Find the height of the flag staff.
Read the following passage:
|
Radio towers are used for transmitting a range of communication services including radio and television. The tower will either act as an antenna itself or support one or more antennas on its structure; On a similar concept, a radio station tower was built in two Sections A and B. Tower is supported by wires from a point O. Distance between the base of the tower and point O is 36 cm. From point O, the angle of elevation of the top of the Section B is 30° and the angle of elevation of the top of Section A is 45°.
|
Based on the above information, answer the following questions:
- Find the length of the wire from the point O to the top of Section B.
- Find the distance AB.
OR
Find the area of ∠OPB. - Find the height of the Section A from the base of the tower.
|
One evening, Kaushik was in a park. Children were playing cricket. Birds were singing on a nearby tree of height 80m. He observed a bird on the tree at an angle of elevation of 45°. When a sixer was hit, a ball flew through the tree frightening the bird to fly away. In 2 seconds, he observed the bird flying at the same height at an angle of elevation of 30° and the ball flying towards him at the same height at an angle of elevation of 60°.
|
- At what distance from the foot of the tree was he observing the bird sitting on the tree?
- How far did the bird fly in the mentioned time?
(or)
After hitting the tree, how far did the ball travel in the sky when Kaushik saw the ball? - What is the speed of the bird in m/min if it had flown `20(sqrt3 + 1) m`?
