Advertisements
Advertisements
प्रश्न
If one looks from a tower 10 m high at the top of a flag staff, the depression angle of 30° is made. Also, looking at the bottom of the staff from the tower, the angle of the depression made is of 60°. Find the height of the flag staff.
उत्तर
In the figure, PQ is the tower of height 10 m and AB is the flagstaff.
∠MPB = ∠PBQ, ∠MPA = ∠PAS ......(Alternate interior angles)
Now, in ΔPBQ
tan 60° = `(PQ)/(BQ)`
⇒ `sqrt(3) = 10/(BQ)`
⇒ BQ = `10/sqrt(3)`
Also, in ΔPAS
tan 30° = `(PS)/(AS)`
⇒ `1/sqrt(3) = (PS)/(BQ)` ......[∵ BQ = AS]
⇒ `1/sqrt(3) = (PS)/(10/sqrt(3)) = (sqrt(3) PS)/10`
⇒ `sqrt(3) xx sqrt(3) PS` = 10
⇒ 3 PS = 10
⇒ PS = `10/3`
So, SQ = AB = PQ – PS
= `10 - 10/3`
= `(3 xx 10 - 10)/3`
= `20/3`
= 6.67
As a result, the flagstaff's height is 6.67 m.
APPEARS IN
संबंधित प्रश्न
A man standing on the deck of a ship, which is 10 m above water level, observes the angle of elevation of the top of a hill as 60° and the angle of depression of the base of a hill as 30°. Find the distance of the hill from the ship and the height of the hill
A vertical tower stands on a horizontal plane and is surmounted by a flagstaff of height 7m. At a point on the plane, the angle of elevation of the bottom of the flagstaff is 30º and that of the top of the flagstaff is 45º. Find the height of the tower.
The angle of elevation of the top of a tower from a point A due south of the tower is α and from B due east of the tower is β. If AB = d, show that the height of the tower is
`\frac{d}{\sqrt{\cot ^{2}\alpha +\cot^{2}\beta `
The elevation of a tower at a station A due north of it is α and at a station B due west of A is β. Prove that the height of the tower is `\frac{AB\sin \alpha \sin \beta }{\sqrt{\sin^{2}\alpha -\sin ^{2}\beta `
A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground, making an angle 30° with it. The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the tree.
An observer finds the angle of elevation of the top of the tower from a certain point on the ground as 30°. If the observe moves 20 m towards the base of the tower, the angle of elevation of the top increases by 15°, find the height of the tower.
If the height of a vertical pole is 3–√3 times the length of its shadow on the ground, then the angle of elevation of the Sun at that time is
(A) 30°
(B) 60°
(C) 45°
(D) 75°
An observer , 1.7 m tall , is` 20 sqrt3` m away from a tower . The angle of elevation from the eye of an observer to the top of tower is 300 . Find the height of the tower.
If the angles of elevation of a tower from two points distant a and b (a>b) from its foot and in the same straight line from it are 30° and 60°, then the height of the tower is
If the angles of elevation of the top of a tower from two points distant a and b from the base and in the same straight line with it are complementary, then the height of the tower is
A tower subtends an angle of 30° at a point on the same level as its foot. At a second point h metres above the first, the depression of the foot of the tower is 60°. The height of the tower is
If a 1.5 m tall girl stands at a distance of 3 m from a lamp-post and casts a shadow of length 4.5 m on the ground, then the height of the lamp-post is
An aeroplane at an altitude of 1800 m finds that two boats are sailing towards it in the same direction. The angles of depression of the boats as observed from the aeroplane are 60° and 30° respectively. Find the distance between the two boats. `(sqrt(3) = 1.732)`
Two ships are sailing in the sea on either side of the lighthouse. The angles of depression of two ships as observed from the top of the lighthouse are 60° and 45° respectively. If the distance between the ships is `200[(sqrt(3) + 1)/sqrt(3)]` metres, find the height of the lighthouse.
The angle of elevation of the top of a tower is 30°. If the height of the tower is doubled, then the angle of elevation of its top will ____________.
A window of a house is h meters above the ground. From the window, the angles of elevation and depression of the top and the bottom of another house situated on the opposite side of the lane are found to be A and B respectively. Then the height of the other house is ____________.
Find the angle of elevation of the sun when the shadow of a pole h metres high is `sqrt(3)` h metres long.
The angles of elevation of the bottom and the top of a flag fixed at the top of a 25 m high building are 30° and 60° respectively from a point on the ground. Find the height of the flag.
We all have seen the airplanes flying in the sky but might have not thought of how they actually reach the correct destination. Air Traffic Control (ATC) is a service provided by ground-based air traffic controllers who direct aircraft on the ground and through a given section of controlled airspace, and can provide advisory services to aircraft in non-controlled airspace. Actually, all this air traffic is managed and regulated by using various concepts based on coordinate geometry and trigonometry.
At a given instance, ATC finds that the angle of elevation of an airplane from a point on the ground is 60°. After a flight of 30 seconds, it is observed that the angle of elevation changes to 30°. The height of the plane remains constantly as `3000sqrt(3)` m. Use the above information to answer the questions that follow-
- Draw a neat labelled figure to show the above situation diagrammatically.
- What is the distance travelled by the plane in 30 seconds?
OR
Keeping the height constant, during the above flight, it was observed that after `15(sqrt(3) - 1)` seconds, the angle of elevation changed to 45°. How much is the distance travelled in that duration. - What is the speed of the plane in km/hr.
