Advertisements
Advertisements
प्रश्न
Due to a heavy storm, a part of a banyan tree broke without separating from the main. The top of the tree touched the ground 15 m from the base making an angle of 45° with the ground. Calculate the height of the tree before it was broken.
उत्तर
Let AC was original tree. Due to storm it was broken into two parts. The broken part A' B is making 45° with ground.
In ΔA'BC
`"BC"/"A'C" = tan 45°`
`"BC"/15 = 1`
BC = 15
`"A'C"/"A'B" = cos 45°`
`15/"A'B" = 1/sqrt(2)`
`A'B = 15sqrt(2)`
`"Height of tree" = A'B + BC = 15 + 15sqrt(2) = 15(1 + sqrt(2)) = 15 × 2.414 = 36.21`
Hence , the height of tree was 36.21 m.
APPEARS IN
संबंधित प्रश्न
From the top of a hill, the angles of depression of two consecutive kilometer stones, due east, are found to be 30° and 45° respectively. Find the distances of the two stones from the foot of the hill.
Calculate AB.
The top of a palm tree having been broken by the wind struck the ground at an angle of 60° at a distance of 9m from the foot of the tree. Find the original height of the palm tree.
From a point 10 m above the ground , the angle of elevation of the top of a tower is α and the angle of depression is β . If tan α = `5/2` and tan β = `1/4` , calculate the height of the tower to the nearest metre .
The horizontal distance between towers is 140 m. The angle of elevation of the top of the first tower when seen from the top of the second tower is 30°. If the height of the second tower is 60m, find the height of the first tower.
The angle of depression of a boat moving towards a diff is 30°. Three minutes later the angle of depression of the boat is 60°. Assuming that the boat is sailing at a uniform speed, determine the time it will take to reach the shore. Also, find the speed of the boat in m/second if the cliff is 450m high.
A man standing on a cliff observes a ship at an angle of depression of the ship is 30°, approaching the shore just beneath him. Three minutes later, the angle of depression of the ship is 60°. How soon will it reach the shore?
A man on the top of a tower observes a truck at an angle of depression ∝ where `∝ = 1/sqrt(5)` and sees that it is moving towards the base of the tower. Ten minutes later, the angle of depression of the truck is found to `β = sqrt(5)`. Assuming that the truck moves at a uniform speed, determine how much more ti me it will take to each the base of the tower?
From the top of a tower 60 m high, the angles of depression of the top and bottom of pole are observed to be 45° and 60° respectively. Find the height of the pole.
Two men on either side of a temple 75 m high observed the angle of elevation of the top of the temple to be 30° and 60° respectively. Find the distance between the two men.
