Advertisements
Advertisements
प्रश्न
The length of the shadow of a pillar is `1/sqrt(3)` times the height of the pillar . find the angle of elevation of the sun .
उत्तर
Let AB be the pillar and BC be its shadow.
Let h be the height of the pillar . Then,
BC = `1/sqrt(3)`h
In ΔABC,
tanθ = `"AB"/"BC"`
⇒ `tanθ = h/(h/sqrt(3)) = sqrt(3)`
But , `tan60^circ = sqrt(3)`
∴ `θ = 60^circ`
APPEARS IN
संबंधित प्रश्न
Two persons are standing on the opposite sides of a tower. They observe the angles of elevation of the top of the tower to be 30° and 38° respectively. Find the distance between them, if the height of the tower is 50 m.
Two vertical poles are on either side of a road. A 30 m long ladder is placed between the two poles. When the ladder rests against one pole, it makes angle 32°24′ with the pole and when it is turned to rest against another pole, it makes angle 32°24′ with the road. Calculate the width of the road.
A man stands 9 m away from a flag-pole. He observes that angle of elevation of the top of the pole is 28° and the angle of depression of the bottom of the pole is 13°. Calculate the height of the pole.
The angle of elevation of the top of a tower is observed to be 60°. At a point, 30 m vertically above the first point of observation, the elevation is found to be 45°. Find:
- the height of the tower,
- its horizontal distance from the points of observation.
Calculate BC.
The radius of a circle is given as 15 cm and chord AB subtends an angle of 131° at the centre C of the circle. Using trigonometry, calculate:
- the length of AB;
- the distance of AB from the centre C.
The angles of depression and elevation of the top of a 12m high building from the top and the bottom of a tower are 60° and 30° respectively. Find the height of the tower, and its distance from the building.
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°?
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)`.
From a lighthouse, the angles of depression of two ships on opposite sides of the lighthouse were observed to be 30° and 45°. If the height of the lighthouse is 90 metres and the line joining the two ships passes through the foot of the lighthouse, find the distance between the two ships, correct to two decimal places.
