Advertisements
Advertisements
प्रश्न
A storm broke a tree and the tree top rested on ground 20 m away from the
base of the tree, making an angle of 60o with the ground. Find the height
of the tree.
उत्तर
AB = Height of the tree
Tree is broken at C
AC = CD ....... (1)
∠ CDB = 60°
BD = 20 m
In right angled Δ CBD,
`tan60° = (CB)/(BD)`
`sqrt3 = (CB)/20`
`CB = 20sqrt3 m.`
`sin60° = (CB)/(CD)`
CD =`sqrt3/2 = (20sqrt3)/(CD)`
`CD = (2 xx 20sqrt3)/sqrt3`
CD = 40 m.
∴ AC = CD = 40 m. ....... (From (1) )
AB = AC + CB
AB = `(40 + 20sqrt3)` m.
∴ height of the tree = `(40 + 20sqrt3)` m.
APPEARS IN
संबंधित प्रश्न
In the following figure, in ΔABC, BC = 1, AC = 2, ∠B = 90°. Find the value of sin θ.
The angle of depression of a car parked on the road from the top of a 150 m high tower is 30°. The distance of the car from the tower (in metres) is
`(A) 50sqrt3`
`(B) 150sqrt 3`
`(C) 150sqrt2`
`(D) 75`
In Fig. 1, AB is a 6 m high pole and CD is a ladder inclined at an angle of 60° to the horizontal and reaches up to a point D of pole. If AD = 2.54 m, find the length of the ladder. (use3√=1.73)
The angles of depression of the top and bottom of a 50 m high building from the top of a tower are 45° and 60° respectively. Find the height of the tower and the horizontal distance between the tower and the building (use `sqrt3`=1.73)
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
A flag-staff stands on the top of a 5 m high tower. From a point on the ground, the angle of elevation of the top of the flag-staff is 60° and from the same point, the angle of elevation of the top of the tower is 45°. Find the height of the flag-staff.
The angle of elevation of the top of an unfinished tower at a distance of 75m from its base is 30° .How much higher must the tower be raised so that the angle of elevation of its top at the same point may be 60 .
From the top of a vertical tower, the angles depression of two cars in the same straight line with the base of the tower, at an instant are found to be 45° and 60° . If the cars are 100 m apart and are on the same side of the tower, find the height of the tower.
Two ships are approaching a light-house from opposite directions. The angles of depression of the two ships from the top of the light-house are 30° and 45°. If the distance between the two ships is 100 m, find the height of the light-house. \[[Use \sqrt{3} = 1 . 732]\]
From the top of the light house, an observer looks at a ship and finds the angle of depression to be 30°. If the height of the light-house is 100 meters, then find how far the ship is from the light-house.
Two buildings are in front of each other on a road of width 15 meters. From the top of the first building, having a height of 12 meter, the angle of elevation of the top of the second building is 30°.What is the height of the second building?
From the top of a tree of height 13 m the angle of elevation and depression of the top and bottom of another tree are 45° and 30° respectively. Find the height of the second tree. `(sqrt(3) = 1.732)`
A statue, 2 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60° and from the same point, the angle of elevation of the top of the pedestal is 45°. Find the height of the pedestal.
A 1.5 m tall boy is standing at some distance from a 31.5 m tall building. If he walks ’d’ m towards the building the angle of elevation of the top of the building changes from 30° to 60°. Find the length d. (Take `sqrt3 = 1.73`)
A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height h. At a point on the plane, the angles of elevation of the bottom and the top of the flagstaff are α and β, respectively. Then the height of the tower is ____________.
If a man standing on a platform 3 metres above the surface of a lake observes a cloud and its reflection in the lake, then the angle of elevation of the cloud is equal to the angle of depression of its reflection.
An observer 1.5 metres tall is 20.5 metres away from a tower 22 metres high. Determine the angle of elevation of the top of the tower from the eye of the observer.
Lakshaman Jhula is located 5 kilometers north-east of the city of Rishikesh in the Indian state of Uttarakhand. The bridge connects the villages of Tapovan to Jonk. Tapovan is in Tehri Garhwal district, on the west bank of the river, while Jonk is in Pauri Garhwal district, on the east bank. Lakshman Jhula is a pedestrian bridge also used by motorbikes. It is a landmark of Rishikesh. A group of Class X students visited Rishikesh in Uttarakhand on a trip. They observed from a point (P) on a river bridge that the angles of depression of opposite banks of the river are 60° and 30° respectively. The height of the bridge is about 18 meters from the river. |
Based on the above information answer the following questions.
- Find the distance PA.
- Find the distance PB
- Find the width AB of the river.
[OR]
Find the height BQ if the angle of the elevation from P to Q be 30°.
We all have seen the airplanes flying in the sky but might have not thought of how they actually reach the correct destination. Air Traffic Control (ATC) is a service provided by ground-based air traffic controllers who direct aircraft on the ground and through a given section of controlled airspace, and can provide advisory services to aircraft in non-controlled airspace. Actually, all this air traffic is managed and regulated by using various concepts based on coordinate geometry and trigonometry.
At a given instance, ATC finds that the angle of elevation of an airplane from a point on the ground is 60°. After a flight of 30 seconds, it is observed that the angle of elevation changes to 30°. The height of the plane remains constantly as `3000sqrt(3)` m. Use the above information to answer the questions that follow-
- Draw a neat labelled figure to show the above situation diagrammatically.
- What is the distance travelled by the plane in 30 seconds?
OR
Keeping the height constant, during the above flight, it was observed that after `15(sqrt(3) - 1)` seconds, the angle of elevation changed to 45°. How much is the distance travelled in that duration. - What is the speed of the plane in km/hr.
The top of a hill when observed from the top and bottom of a building of height h is at angles of elevation p and q respectively. What is the height of the hill?
