Advertisements
Advertisements
प्रश्न
Two climbers are at points A and B on a vertical cliff face. To an observer C, 40 m from the foot of the cliff, on the level ground, A is at an elevation of 48° and B of 57°. What is the distance between the climbers?
उत्तर
Let P be the foot of the cliff on level ground.
Then, ∠ACP = 48° and ∠BCP = 57°
∴ `(BP)/(PC) = tan 57^circ`
`=>` BP = 40 × 1.539 = 61.57 m
Also, `(AP)/(PC) = tan 48^circ`
`=>` AP = 40 × 1.110 = 44.4 m
Hence, distance between the climbers = AB = BP – AP = 17.17 m
APPEARS IN
संबंधित प्रश्न
A man standing on the bank of a river observes that the angle of elevation of a tree on the opposite bank is 60°. When he moves 50 m away from the bank, he finds the angle of elevation to be 30°.
Calculate :
- the width of the river;
- the height of the tree.
The distance of the gate of a temple from its base is `sqrt(3)` times it height. Find the angle of elevation of the top of the temple.
The angle of elevation of the top of a vertical cliff from a point 30 m away from the foot of the cliff is 60°. Find the height of the cliff.
A 10 m high pole is kept vertical by a steel wire. The wire is inclined at an angle of 40° with the horizontal ground. If the wire runs from the top of the pole to the point on the ground where Its other end is fixed, find the lenqth of the wire.
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.
An aeroplane at an altitude of 200 m observes the angles of depression of opposite points on the two banks of a river to be 45° and 60°. Find the width of the river.
The angle of elevation of a tower from a point 200 m from its base is θ, when `tan θ = 2/5`. The angle of elevation of this tower from a point 120m from its base is `Φ`. Calculate the height of tower and the value of `Φ`.
If the angle of elevation of a cloud from a point h m above a lake is α, and the angle of depression of its reflection in the lake be β, prove that distance of the cloud from the point of observation is `("2h"secα)/(tanα - tanβ)`.
A man is standing on the deck of a ship, which is 10 m above water level. He observes the angle of elevation of the top of a hill as 60° and the angle of depression of the base of the hill as 30°. Calculate the distance of the hill from the ship and the height of the hill.
The angle of elevation of the top of a 100 m high tree from two points A and B on the opposite side of the tree are 52° and 45° respectively. Find the distance AB, to the nearest metre.
