Advertisements
Advertisements
प्रश्न
A statue, 1.6 m tall, stands on a top of pedestal, from a point on the ground, the angle of elevation of the top of statue is 60° and from the same point the angle of elevation of the top of the pedestal is 45°. Find the height of the pedestal.
उत्तर
Let AB be the statue, BC be the pedestal, and D be the point on the ground from where the elevation angles are to be measured.
In ΔBCD,
`("BC")/("CD")` = tan 45°
`("BC")/("CB")` = 1
BC = CD
In ΔACD,
`("AB"+"BC")/("CD")` = tan 60°
`("AB"+"BD")/("BC") = sqrt3`
`1.6+"BC" = "BC"sqrt3`
`"BC"(sqrt3-1) = 1.6`
BC = `((1.6)(sqrt(3)+1))/((sqrt(3)-1)(sqrt(3)+1))`
= `(1.6(sqrt(3)+1))/((sqrt(3))^2-(1)^2)`
= `(1.6(sqrt3+1))/2`
= `0.8(sqrt3+1)`
Therefore, the height of the pedestal is 0.8 `(sqrt3+1)` m.
संबंधित प्रश्न
The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are 60° and 30° respectively. Find the height of the tower.
A 21 m deep well with diameter 6 m is dug and the earth from digging is evenly spread to form a platform 27 m ✕ 11 m. Find the height of the platform.[Use `pi=22/7`]
The shadow of a tower, when the angle of elevation of the sun is 45°, is found to be 10 m. longer than when it was 600. Find the height of the tower.
The angle of elevation of an aeroplane from a point on the ground is 45°. After a flight of 15 seconds, the elevation changes to 30°. If the aeroplane is flying at a height of 3000 metres, find the speed of the aeroplane.
A man on the deck of a ship, 16m above water level, observe that that angle of elevation and depression respectively of the top and bottom of a cliff are 60° and 30° . Calculate the distance of the cliff from the ship and height of the cliff.
The angle of elevation of an aeroplane from a point on the ground is 45° after flying for 15seconds, the elevation changes to 30° . If the aeroplane is flying at a height of 2500 meters, find the speed of the areoplane.
The tops of two towers of height x and y, standing on level ground, subtend angles of 30º and 60º respectively at the centre of the line joining their feet, then find x : y.
A man is standing on the deck of a ship, which is 40 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 `(sqrt(3) = 1.732)`
The angle of elevation of the top of a cell phone tower from the foot of a high apartment is 60° and the angle of depression of the foot of the tower from the top of the apartment is 30°. If the height of the apartment is 50 m, find the height of the cell phone tower. According to radiation control norms, the minimum height of a cell phone tower should be 120 m. State if the height of the above mentioned cell phone tower meets the radiation norms
The angles of elevation and depression of the top and bottom of a lamp post from the top of a 66 m high apartment are 60° and 30° respectively. Find the difference between height of the lamp post and the apartment
The angle of depression of the top and bottom of 20 m tall building from the top of a multistoried building are 30° and 60° respectively. The height of the multistoried building and the distance between two buildings (in metres) is
At some time of the day, the length of the shadow of a tower is equal to its height. Then, the sun’s altitude at that time is ______.
In given figure, the length of AP is ____________.
An electrician has to repair an electric fault on a pole of height 4 m. He needs to reach a point 1.3 m below the top of the pole to undertake the repair work. What should be the length of the ladder that he should use which when inclined at an angle of 60° to the horizontal would enable him to reach the required position?
A kite is flying at a height of 30 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60°. Find the length of the string, assuming that there is no slack in the string.
A pole of height 30 m is observed from a point. The angle of depression of the point is 30°. Find the distance of the point from the base of the pole.
From the top of building AB, a point C is observed on the ground whose angle of depression is 60° and which is at a distance of 40 m from the base of the building. Complete the following activity to find the height of building AB.
From figure, BC = `square`, ∠ACB = `square`
In ΔACB,
tan `square = square/(BC)`
⇒ `square = square/square`
⇒ `square = square`
Hence, the height of the building AB is `square`.
The top of a hill when observed from the top and bottom of a building of height h is at angles of elevation p and q respectively. What is the height of the hill?
From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 30°. Determine the height of the tower.
The angle of elevation of the top of a 15 m high tower at a point `15sqrt(3)` m away from the base of the tower is ______.
