The length of side AB and side BC of a scalene triangle ABC are 12 cm and 8 cm respectively The valu...........

Quantitative Aptitude ( CCS) Geometry

The length of side AB and side BC of a scalene triangle ABC are 12 cm and 8 cm respectively. The value of angle C is 59°. Find the length of side AC.

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Explanation:

Given, AB = 12 cm, BC = 8 cm,
∠C = 59°
Let ∠A = Θ
∴ ∠B = 180° – (59° + Θ) = 121° – Θ
Now, let us see the choices. If AC = 12 cm, triangle would not be scalene. Hence, option A is ruled out. If AC = 10 cm, AB will become the largest side and ∠C the largest angle. But ∠C = 59°. Hence option B is ruled out. So, AC is either 14 cm or 16 cm. In any case, ∠B will be the largest angle and ∠A (say Θ) the smallest:
Also, ∠B = 180° – (59° + Θ) = 121° – Θ
By sine formula,