A school authority constructed a slide for its children below the age of 12 years. The constructed slide has a height of 4 m above the ground and is inclined at an angle of 30 to the ground. Use the given information to answer each of the following : (i) the length of slide AB is : (a) 8 m (b) 6 m (c) 5 m (d) 10 m (ii) the value of sin2 30 + cos2 60 is : (a) (b) (c) (d) (iii) if cos A = , then the value of 12 cot2 A - 2 is : (a) 5 (b) 4 (c) 3 (d) 2

Question

KnowledgeBoat · Accepted Answer

Given, Height = 4 m Angle with the ground = 30 (i) Calculating, ⇒ sin 30 = ⇒ ⇒ AB = 4 × 2 = 8 m. Length of slide = 8 m. Hence, option (a) is the correct option. (ii) We know that: sin 30 = and cos 60 = sin2 30 + cos2 60 Hence, option (b) is the correct option. (iii) Given, cos A = So, A = 60 sin A = According to the question, 12 cot2 A - 2 = 12 - 2 = 12 × - 2 = 4 - 2 = 2. Hence, option (d) is the correct option.

Mathematics

Trigonometric Identities

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