This CBSE class 10 Maths extra question is from the topic 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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Δ ABC is right angled at B

AB = 12 cm and ∠CAB = 60 °

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 **

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 **

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CBSE Class 10 Maths - 2021

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