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

AB = 5 cm and AC = 10 cm

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°**

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° **

Class 10 Maths

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CBSE Class 10 Maths - 2020

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