Maths -Quadratic Equation and Trignometric Identities Class 10th
Mathematics
Quadratic Equation and Application of Trigonometry
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Que:- Solve the quadratic Equation by factorization method:-
1.x/x+1 +x+1/x=34/15 ,x≠0,x≠-1
2.1/x-2 +2/x-1 =6/x
3.x+3/x-2 - 1-x/x =17/4
4. 4/x -3 =5/2x+3 (x≠0,-3/2)
5. 2x/x-3 + 1/2x+3 +3x+9/(x-3) (2x+3) =0
6. x^2-2ax +a^2-b^2 =0
7. 4x^2 -4ax +(a^2-b^2)=0
8.x^2-4ax +4a^2 -b^2=0
9.x^2+(a/a+b +a+b/a)x+1=0
10. x^2+x-(a+1) (a+2) =0
Que:-Application of Trigonometry questions are as follow:-
1.A bridge across a river makes an angle of
45° with the river bank as shown in figure .1.1.If the length of the bridge across the river is 150m,what is the width of the river?
Fig:-1.1
3.The angle of elevation of the top Q of a vertical tower PQ from a point X on the ground is 60°.At a point Y ,40m vertically above X ,the angle of elevation is 45°.Find the height of the tower PQ and the dstance XQ.
4.From a window 15metres high above the ground in a street,the angles of elevation and depression of the top and the foot of another house on the opposite side of the street are 30° and 45° respectively show that the height of the opposite house is 23.66 metres(Take √3=1.732).
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5.A man standing on the deck of a ship,which is 10m 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 from the ship and the height of the hill.
6.The angle of elevation of a jet plane from a point A on the ground is 60°.After a flight of 30 seconds ,the angle of elevation changes to 30°.If the jet plane is flying at a constant height of 3600√3 ,find the speed of the jet plane.
7.If the angle of elevation of a cloud from a point h metres above a lake is alpha and the angle of depression of it's reflection in the lake is bita ,prove that the height of the cloud is
h(tan bita +tan alpha)/tan bita-tan alpha
8.The angle of elevation of a cloud from a point 60m above a lake is 30° and the angle of depression of the reflection of cloud in the lake is 60° .Find the height of the cloud.
9. A round balloon of radius r sutends an angle alpha at the eye of the observer while the angle of elevation of it's centre is bita .Prove that the height of the centre of the balloon is
r sin bita .cosec alpha/2.
10.The angle of elevation of a cliff from a fixed point is thita.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 alpha .Show that the height of the cliff is :-
k(cos∅-sin∅cot alpha)/cot∅-cot alpha metres.
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By Anuranjan Gadekar
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