Extra Questions For Class 10 Maths Trigonometry | Q7

This CBSE class 10 Maths extra question is from the chapter Introduction to Trigonometry. Concept Covered: Calculating trigonometric ratios of specific values.

Question 7: In triangle ABC right angled at B, AB = 12cm and ∠CAB = 60°. Determine the lengths of the other two sides.

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Video Explanation

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Explanatory Answer | Trigonometry Extra Question 7

Δ ABC is right angled at B
AB = 12 cm and ∠CAB = 60 °

Part 1: Compute Length of AC

Let us use the trigonometric ratio involving AB and AC.
To angle ∠CAB, AB is the adjacent side.
AC is the hypotenuse of the triangle.
So, we will use cos ∠CAB.

cos ∠CAB = cos 60° = \\frac{\text{AB}}{\text{AC}})
cos 60° = \\frac{\text{1}}{\text{2}})
∴ \\frac{\text{1}}{\text{2}}) = \\frac{\text{12}}{\text{AC}})
AC = 2 × 12 = 24 cm
So, AC = 24 cm

Part 2: Calculate Length of BC

Let us use the trigonometric ratio involving AB and BC.
To angle ∠CAB, AB is the adjacent side and BC is the opposite side.
So, we will use tan ∠CAB

tan ∠CAB = tan 60 ° = \\frac{\text{BC}}{\text{AB}})
tan 60° = √3
√3 =\\frac{\text{BC}}{\text{12}})
BC = 12 × √3 cm