Advertisements
Advertisements
प्रश्न
A vertical tower stands on a horizontal plane and is surmounted by a flagstaff of height 7 meters. At a point in a plane, the angle of elevation of the bottom and the top of the flagstaff are respectively 30° and 60°. Find the height of the tower.
उत्तर
Let the height of the tower be x m and distance DC = y m.
∴ AB = height of flagstaff = 7 m
Now in right-angled Δ BCD,
`"BC"/"CD" = tan 30°`
∴ `x/y = 1/sqrt3`
⇒ y = √3x ....(i)
Also, in right angled Δ ACD,
`"AC"/"CD" = tan 60°`
⇒ `(x + 7)/y = sqrt3`
⇒ x + 7 = √3y
⇒ x + 7 = 3(√3 x) ...(from (i))
⇒ x + 7 = 3x
⇒ 2x = 7
⇒ x = `7/2` = 3.5 m
APPEARS IN
संबंधित प्रश्न
The horizontal distance between two towers is 120 m. The angle of elevation of the top and angle of depression of the bottom of the first tower as observed from the second tower is 30° and 24° respectively.
Find the height of the two towers. Give your answer correct to 3 significant figures
Find the height of a building, when it is found that on walking towards it 40 m in a horizontal line through its base the angular elevation of its top changes from 30° to 45°.
Calculate AB.
The top of a ladder reaches a pcint on the wall 5 m above the ground. If the foot of the ladder makes an angle of 30° with the ground, find the length of the ladder.
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.
The angle of elevation of the top of an unfinished tower at a point 150 m from its base is 30°. How much higher must the tower be raised so that its angle of elevation at the same point may be 60°?
The horizontal distance between two trees of different heights is 100m. The angle of depression of the top of the first tree when seen from the top of the second tree is 45°. If the height of the second tree is 150m, find the height of the first tree.
Two boats approaching a light house in mid sea from opposite directions observe the angle of elevation of the top of the light house as 30° and 45° respectively. If the distance between the two boats is 150m, find the height of the light house.
A man on the deck of a ship is 10 m above water level. He observes that the angle of elevation of the top of a cliff is 42° and the angle of depression of the base is 20°. Calculate the distance of the cliff from the ship and the height of the cliff.
A vertical tower standing on a horizontal plane is surmounted by a vertical flagstaff. At a point 100 m away from the foot of the tower, the angle of elevation of the top and bottom of the flagstaff are 54° and 42° respectively. Find the height of the flagstaff. Give your answer correct to nearest metre.
