(a) A triangle has sides a = 2 and b = 3 and angle C = 60. Find i. the length of side c. ii. Find the sine of angle B using sine rules. (b) If we have a triangle which has one of its side c = 2 and angles A = ?/4 and B = ?/3. Workout the length a of the side opposite A.
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Using the cosine rule: \[ c^2 = a^2 + b^2 - 2ab \cdot \cos(C) \] \[ c^2 = 2^2 + 3^2 - 2(2)(3) \cdot \cos(60^\circ) \] \[ c^2 = 4 + 9 - 12 \cdot \frac{1}{2} \] \[ c^2 = 13 - 6 \] \[ c^2 = 7 \] \[ c = \sqrt{7} \] Show more…
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