Archives

If sin A : sin B : sin C = 3 : 4 : 5, then cos A : cos B is equal to

1) 4 : 3 2) 5 : 3 3) 3 : 4 4) 3 : 5 Solution: Given sin A : sin B : sin C = 3 : 4 : 5 Let sin A = 3x, sin B = 4x, sin C = 5x By sine rule... View Article

The angles of a triangle are in the ratio 3 : 5 : 10. Then, the ratio of the smallest side to the greatest side is

1) 1 : sin 10o 2) 1 : 2 sin 100 3) 1 : cos 10o 4) 1 : 2 cos 10o Solution: Given the angles of a triangle are in the ratio 3 : 5 : 10. Let A... View Article

In a ∆ABC, b = √3, c = 1 and ∠A = 30^o, then the largest angle of the triangle is

1) 60o 2) 135o 3) 90o 4) 120o Solution: Given b = √3, c = 1 and ∠A = 30o cos A = (b2 + c2 -a2)/2bc √3/2 = (√32 + 12 - a2)/2√3 √3/2 = (4 -... View Article

The area of the ∆ ABC, in which a = 1, b = 2, ∠C = 60^o, is

1) 4 sq units 2) 1/2 sq units 3) √3/2 sq units 4) √3 sq units Solution: Given a = 1, b = 2, ∠C = 60o We know area of ∆ ABC = ½ ab sin C = ½... View Article

In a ∆ABC, if b + c = 2a and ∠A = 60^o, then ∆ABC is

1) equilateral 2) right angled 3) isosceles 4) scalene Solution: Given b + c = 2a Using sine rule k sin B + k sin C = 2k sin A sin B + sin C... View Article

If in a ∆ ABC, a = 15, b = 36, c = 39, then sin C/2 is equal to

1) √3/2 2) 1/2 3) 1/√2 4) - (1/√2) Solution: Given a = 15, b = 36, c = 39 We know sin (C/2) = √((s-a)(s-b)/ab) Here s = (a + b + c)/2 = (15... View Article

If in ∆ABC, (b+c)/11 = (c+a)/12 = (a+b)/13, then cos A is equal to

(1) 1/5 (2) 5/7 (3) 19/35 (4) none of these Solution: Let (b + c)/11 = (c + a)/12 = (a + b)/13 = x b + c = 11 x, c + a = 12 x, a + b = 13x... View Article

In ∆ABC, (a + b + c)(tan (A/2) + tan (B/2)) is equal to

(1) 2c cot C/2 (2) 2a cot A/2 (3) tan C/2 (4) none of these Solution: We know s = (a + b + c)/2 tan (A/2) = √[(s - b)(s-c)/s(s-a)] (a + b +... View Article

If two angles of ∆ABC are 45^o and 60^o, then the ratio of the smallest and the greatest sides are

1) (√3 - 1) : 1 2) √3 : √2 3) 1 : √3 4) √3 : 1 Solution: Let A = 450 and B = 600. So 3rd angle, C = 180 - (45 + 60) = 750 We know that the... View Article

If in a ∆ABC , a = 6 cm , b = 8 cm , c = 10 cm, then the value of sin 2A is

1) 6/25 2) 8/25 3) 10/25 4) 24/25 Solution: Given a = 6 cm , b = 8 cm , c = 10 cm From cosine rule cos A = (b2 + c2 - a2)/2bc = (82 + 102 -... View Article

The area (in sq units) of the triangle whose sides are 6, 5, √13, is

1) 5√2 2) 9 3) 6√2 4) 11 Solution: Let the sides be a = 6, b = 5, c = √13. cos C = (a2 + b2 - c2)/2ab = (62 + 52 - √132)/2×6×5 = (36 + 25 -... View Article

The sides of a triangle are respectively 7 cm, 4√3 cm and √13 cm, then the smallest angle of triangle is

1) π/6 2) π/3 3) π/4 4) π/5 Solution: Given sides of a triangle are respectively 7 cm, 4√3 cm and √13 cm. Here smallest side = √13 We know... View Article

In any ∆ABC, the simplified form of (cos 2A/a²) – (cos 2B/b²) is

1) a2 - b2 2) 1/(a2 - b2) 3) 1/a2 - 1/b2 4) a2 + b2 Solution: We know cos 2θ = 1 - 2 sin2 θ (cos 2A/a2) - (cos 2B/b2) = (1 - 2 sin2 A)/a2 -... View Article

If the sides of a right angled triangle form an AP, then the ‘sin’ of the acute angles are

(1) ⅗, ⅘ (2) ⅕, ⅖ (3) √3, 1/√3 (4) none of these Solution: Let the sides of the triangle be (a - d), a, (a + d) Applying pythagoras theorem... View Article

If the angles A, B and C of a triangle are in an arithmetic progression and if a, b and c denote the lengths of the sides opposite to A, B and C respectively, then the value of the expression (a/c) sin 2C + (c/a) sin 2A is

1) 1/2 2) √3/2 3) 1 4) √3 Solution: Given angles of a triangle ABC are in AP. Let a-d, a, a+d represent angles A, B and C. a-d + a + a+d =... View Article