SOME APPLICATION OF TRIGONOMERTY

REMEMBER TO POINTS :-

1.                                              

/ T-RATIONS	00	300	450	600	900
SIN	0	1/2	1/√2	√3/2	1
COS	1	√3/2	1/√2	1/2	0
TAN	0	1/√3	1	√3	N.D
COT	N.D	√3	1	1/√3	0
SEC	1	2/√3	√2	2	N.D
COSEC	N.D	2	√2	2/√3	1

2.   PANDIT BADIRI PRASHAND        P FOR PENDICULAR  S FOR SIN

  HAR HAR BHOLE               B FOR BASE       C FOR COS    SONA CHADI TOLE              H FOR HYP        T FOR TAN

                            Pervious year question

Q.1 The angles of elevation of the top of a tower from two points P and Q at distances 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 √ab.

Q.2 At a point on the level ground, the angle of elevation of a vertical tower is found to be such that its tangent is .On walking 192 meters towards the tower, the tangent of the angle of elevation is .find the height of the tower.

Q.3 The shadow of a tower, standing on the level ground, is found to be 45 m longer when sun’s altitude is 30^o,then when it was at 60^o.find the height of the tower.

Q.4 Determine the height of a mountain if the elevation of its top at an unknown distance from the base is 60^o and at a distance 10Km further off from the mountain, along the same line, the angle of elevation is 30^o.

Q.4 A straight highway leads to the foot of a tower of height 50m. from the top of the tower the angle of depression of two cars standing on the highway are 30^o and 60^o.what is the distance between the two cars and how far is each car from the tower ?

Q.5 From the top of a hill, the angle of depression of two consecutive kilometer stones due east are found to be 30^o and 45^o. find the height of the hill.

Q.6 An aero plane at an altitude of 1200 m finds that two ships are sailing towards it in the same direction. the angles of depression of the ships as observed from the aero plane are 60^o and 30^o respectively .find the distance between the two ships.

Q.7 An aeroplane when flying at a height of 4000 m from the ground passes vertically above another aeroplane at an instant when the angles of the elevation of the two planes from the same points on the ground are 60^o and 45^o respectively. Find the vertical distance between the aeroplanes at that instant.

Q.8 two boats approach a light house in mid-sea from opposite directions. The angle of elevation of the top of the light house from two boats is 30^o and 45^o respectively. If the distance between two boats is 100 m, find the height of light house.

Q.9 from the top of a light house , the angles of depression of two ships on the opposite sides of it are observed to be  and . If the height of the light house be h meters and the line joining the ships passes through the foot of the light house, show that the distance between the ships is  metres.

Q.10 A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height h .At a point on the plane, the angles of elevation of the bottom and the top of the flagstaff are α and β respectively. Prove that the height of the tower is  .

Q.11 From a window (60 meters high above the ground) of a house in a street the angle of elevation and depression of the top and the foot of another house an opposite side of street are 60^o and 45^o respectively. Show that the height of the opposite house is 60(1+ √3) metres.

Q.12 A man is standing on the deck of a ship , which is 10m above water level. He observes that the angle of elevation of the top of hill as 60^o and the angle of depression of the base as 30^o .calculate the distance of the hill from the ships.

Q.13 the angle of elevation of the cloud from a point 60m above a lake is 30^o and the angle of depression of the reflection of cloud in the lake is 60^o .find the height of the cloud.

Q.14 if the angle of elevation of cloud from a point h metre above a lake is α and angle of depression of its reflection in the lake is β, prove that the height of the cloud above lake level is .

Q.15 the angle of elevation of a jet plane from a point A on the ground is 60^o. after flight of 15 second , the angle of elevation change to 30^o.if the jet is flying at a constant height of 1500√3 m, find the speed of the jet plane.

Q.16 A round balloon of radius r subtends an angle α at the eye of the observer while the angle of elevation of its centre is β. Prove that the height of the centre of the balloon is r sin β cosec α/2.

Q.17 At the foot of a mountain the elevation of its summit is 45^o, after ascending 1000m towards the mountain up a slope of 30^o inclination, the elevation is found to be 60^o.find the height of the mountain.

Q.18 The angle of elevation of a cliff from point is θ. After going up a distance of k metres towards the top of the cliff at an angle of ∅, it is found that the angle of elevation is α, then show that height of the cliff is metres.

Q.19 Two stations due south of a leaning tower which leans towards the north are at distance ‘a’ and ‘b’ from the foot. If α,β be the elevations of the top of tower from these stations , prove that its inclination θ to the horizontal is given by

                  cot θ =

Q.20 A man standing ‘a’ metre behind and opposite of a foot ball goal observes that the angle of elevation of nearer cross bar is α that of the further cross bar is β. show that the length of the field is  or a(tanα cotβ-1).

Q.21 A tower in a city centre is 150m high and a multistory hotel at the city centre is 20m high. the angle of elevation of the top of the tower at the top of the hotel is 5^o. a building ‘h’ metre high, is situated of the top of the straight road connecting the tower with the city centre,at a distances of 1.2km from the tower. Find the value of ‘h’ if top of the hotel, top of the building and the top of the tower are in a straight line. Also, find the distance of the tower from the city centre.[use tan 5^o=.0875, tan 85^o=11.43]

Q.22 the angle of elevation of the top of a tower from a points 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  .

Q.23 the elevation of a tower at a station A due north of it is α and at a station B due east of A is β.prove that the height of the tower is AB sinα sinβ/√sin²α-sin²β.

Q.24 A fire at a building B is reported on telephones to two fire stations F₁ and F₂ 10km apart from each other on a straight road . F₁ observes that the fire is at an angle of 60^o to the road and F₂ observes that it is at an angle of 45^o from it. Which station should send his team and how much will it have to travel?

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