Advertisements
Advertisements
प्रश्न
Two persons standing on opposite sides of a tower observe the angles of elevation of the top of the tower to be 60° and 50° respectively. Find the distance between them, if the height of the tower is 80m.
उत्तर
Let the position of the two persons be A and C. Let BD be the tower of height 80 m.
In ΔBAD,
`tan60^circ = "BD"/"AD"`
⇒ `sqrt(3) = 80/"AD"`
⇒ `"AD" = 80/sqrt(3)`
⇒ AD = `(80sqrt(3))/3 = (80 xx 1.732)/3` = 46.19 ...(1)
In ΔBDC,
`tan50^circ = "BD"/"DC"`
⇒ `1.1918 = 80/"DC"`
⇒ `"DC" = 80/1.1918 = 67.13` ....(2)
:. AC = AD + DC = 46.19 m + 67 .13 m = 113.32 m
Thus, the horizontal distance between the two persons is 113. 32 m.
APPEARS IN
संबंधित प्रश्न
Find the height of a tree when it is found that on walking away from it 20 m, in a horizontal line through its base, the elevation of its top changes from 60° to 30°.
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°.
A person standing on the bank of a river observes that the angle of elevation of the top of a tree standing on the opposite bank is 60°. When he moves 40 m away from the bank, he finds the angle of elevation to be 30°. Find:
- the height of the tree, correct to 2 decimal places,
- the width of the river.
Find AD.
Calculate BC.
The angles of elevation of the top of a tower from two points on the ground at distances a and b metres from the base of the tower and in the same straight line with it are complementary. Prove that the height of the tower is `sqrt(ab)` metre.
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.
An observer point for ships moving in the sea 500m above the sea level. The person manning this point observes the angle of depression of twc boats as 45° and 30°. Find the distance between the boats when they are on the same side of the observation point and when they are on opposite sides of the observation point.
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?
The angles of elevation of the top of a tower from two points A and B at a distance of a and b respectively from the base and in the same straight line with it are complementary. Prove that the height of the tower is `sqrt(ab)`.
