Extra Questions For Class 10 Maths Chapter 8 | Q8

Trigonometry | Trigonometric Values of Basic angles

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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Explanatory Answer | Trigonometry Extra Question 8

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

CBSE Class 10 Trigonometry Q8 Triangle

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°

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