Trigonometry Extra Question 8

This CBSE class 10 Maths extra question is from the chapter Introduction to Trigonometry. It tests the concept of computing angles from values of trigonometric ratios computed from the measures of the sides of a right triangle.

Question 8: In a triangle ABC right angled at B, AB = 5 cm and AC = 10 cm. Determine ∠ BAC and ∠ BCA.

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Video Explanation

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Explanatory Answer | Trigonometry Extra Question 8

Δ ABC is right angled at B
AB = 5 cm and AC = 10 cm

Step 1: Calculate ∠BCA

AB is the opposite side and AC is the hypotenuse to the triangle.
∴ We will use sin ∠BCA = \\frac{\text{AB}}{\text{AC}})= \\frac{\text{5}} {\text{10}})=\\frac{\text{1}}{\text{2}})

We know sin 30° = \\frac{1}{2})

∴ sin ∠BCA = sin 30° or ∠ BCA = 30°
So, ∠BCA = 30°

Step 2: Calculate ∠BAC

In any triangle, sum of the interior angles is 180°
i.e., ∠ABC + ∠BCA + ∠BAC = 180°
90° + 30° + ∠BAC = 180°
∠BAC = 60°
So, ∠BAC = 60°