Advertisements
Advertisements
प्रश्न
A tree breaks due to the storm and the broken part bends so that the top of the tree touches the ground making an angle of 30° with the ground. The distance from the foot of the tree to the point where the top touches the ground is 10 metres. Find the height of the tree.
उत्तर
Let AB be the tree of height h. And the top of the tree makes an angle of 30° with the ground. The distance between the foot of the tree to the point where the top touches the ground is 10 M.
lET bc = 10 And ∠ACB = 30°
Here we have to find the height of the tree.
Here we have the corresponding figure
So we use trigonometric ratios.
In a triangle ABC
`=> tan C = (AB)/(BC)`
`=> tan 30^@ = (AB)/((BC)`
`=> 1/sqrt3 = h/10`
`=> h = 10/sqrt3`
Now in triangle ABC we have
`sin 30^@ = h/(AC)`
`=> 1/2 = 10/(sqrt3 AC)`
`=> AC = 20/sqrt3`
So the length of the tree is
` = AB + AC`
= h + AC
`= 10/sqrt3 + 20/sqrt3`
`= 10sqrt3`
= 1.73
Hence the height of tree is 17.3 m
APPEARS IN
संबंधित प्रश्न
A truck covers a distance of 150 km at a certain average speed and then covers another 200 km at an average speed which is 20 km per hour more than the first speed. If the truck covers the total distance in 5 hours, find the first speed of the truck.
From a point P on the ground the angle of elevation of the top of a tower is 30° and that of the top of a flag staff fixed on the top of the tower, is 60°. If the length of the flag staff is 5 m, find the height of the tower.
A boat is being rowed away from a cliff 150m high. At the top of the cliff the angle of depression of the boat changes from 60º to 45º in 2 minutes. Find the speed of the boat.
A tower subtends an angle 𝛼 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
The angle of elevation of an aeroplane from a point on the ground is 45° after flying for 15seconds, the elevation changes to 30° . If the aeroplane is flying at a height of 2500 meters, find the speed of the areoplane.
A boy standing at a distance of 48 meters from a building observes the top of the building and makes an angle of elevation of 30°. Find the height of the building.
From the top of a rock `50sqrt(3)` m high, the angle of depression of a car on the ground is observed to be 30°. Find the distance of the car from the rock
A plane is observed to be approaching the airport. It is at a distance of 12 km from the point of observation and makes an angle of elevation of 60°. The height above the ground of the plane is ____________.
A contractor plans to install two slides for the children to play in a park. For the children below the age of 5 years, she prefers to have a slide whose top is at a height of 2m and is inclined at an angle of 30° to the ground. What should be the length of the slide?
A person is standing at a distance of 50 m from a temple looking at its top. The angle of elevation is 45°. Find the height of the temple.
