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All India-2018
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Q27 of 30 Page 1

Prove that:


Proof:

LHS=



(Taking SinA common from numerator and cosA common from denominator)


⇒


Replacing 1 with




⇒ tanA


= RHS


Hence, proved.

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25

In an equilateral ∆ABC, D is a point on side BC such that . Prove that 9(AD)2 = 7(AB)2

OR


Prove that, in a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides.

26

Draw a triangle ABC with BC = 6 cm, AB = 5 cm and ∠ ABC = 60°. Then construct a triangle whose sides are 3/4 of the corresponding sides of the ∆ ABC.

28

The diameters of the lower and upper ends of a bucket in the form of a frustum of a cone are 10 cm and 30 cm respectively. If its height is 24 cm, find :

(i) The area of the metal sheet used to make the bucket.


(ii) Why should we avoid the bucket made by ordinary plastic? [Use π = 3.14]

29

As observed from the top of a 100m high light house from the sea - level, the angles of depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the light house, find the distance between the two ships. [Use 3 = 1.732]

Questions · 30
All India-2018
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