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CHAPTER 5, TRIGONOMETRY, ANGLES AND SIDES, , * If the angles of a triangle are 45°, 45°, 90° , the opposite sides are in the, ratio 1 : 1: √2, , eg: -, , * If the angles are 30° , 60° , 90° . then opposite sides are in the ratio 1: √ 3 :, 2, , :, here the side, opposite to 60° is = 3√3

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Q) find the ratio of the sides of the triangle shown below., , By drawing the perpendicular from the top vertex to the base, we get two right triangles, , AB = √2x, AC = 2x, BD = x, CD = √3x, BC = x + √3x, = x ( 1 + √3 ), Here the sides are =, √2x , 2x , x(1+√3), So the ratio = √2 : 2 : ( 1 + √ 3 ), Q) In the triangle shown, what is the perpendicular distance from the top, vertex to the bottom side? What is the area of the triangle?, , Ans: here ∆ABC is isosceles , AD divides ∆ ABC equally, AD= side opposite to 30° = 1 cm, BD = side opposite to 60° = √3 cm

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BC = 2√3, Area = ½ bh, Area = ½ × 2√ 3 × 1, √ 3 cm2, Q) The diagonal of a square is 4cm long . Find its perimeter and area?, , Ans: - Angles of ∆ABC are 45° , 45° , 90°, therefore sides are in the, ratio 1: 1: √2, AC = 4cm, that is √2x = 4, x=4, √2, 2, Area = 4, √22, = 16, 2, = 8cm2, Perimeter = 2( l + b), = 2 ( 4/√ 2 + 4/√2 ), = 2 ( 8/√2) = 2× 8√2, = 16, √2, = 8× 2, √2, = 8 × √2 ×√ 2, √2, = 8√2 cm, , Q)

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Ans :-, , here CD is perpendicular to AB, Angles of ∆ ADC are 30° ,60° , 90°, The sides are x , √3x , 2x, so the sides are in the ratio, 1 : √3 : 2, here 2x = 12cm, so ,x = 12, 2, = 6cm, CD = 6cm, b ) Area of ∆ ABC = ½ × 20 × 6, = 60cm2, NEW MEASURE OF ANGLES, Sin , Cosine , Tan, , Sin = opposite side, hypotenuse, Cos = Adjacent side, hypotenuse

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Tan = opposite side, Adjacent side, , sin 45° = 1, √2, Cos 45° = 1, √2, tan 45° = 1, , sin 30° = ½, cos 30° = √3, 2, tan30° = 1, √3, , ANGLES, , 0°, , sin 60° = √3, 2, cos 60° = ½, tan60° = √3, 1, , 30°, , 45°, , 60°, , 90°

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Sin, , 0, , ½, , 1, √2, , √3, 2, , 1, , Cos, , 1, , √3, 2, , 1, √2, , ½, , 0, , Tan, , 0, , 1, √3, , 1, , √3, , Not, difin, ed, , Q) Given below are the hypotenuse and one angle of some right triangles., Find the other sides length., Hypotenuse, , one, angle, , sin, value, , cos, value, , a, , 10, , 15°, , .2588, , .9659, , b, , 12, , 25°, , .4226, , .9063, , c, , 8, , 40°, , .6428, , .7660, , d, , 10, , 75, , .9659, , .2588