Question

The sines of two angles of a triangle are equal to 5/13 and 99/101. The cosine of the third angle is

• A. $\frac{255}{1315}$
• B. $\frac{251}{1313}$
• C. $\frac{255}{1313}$
• D. None of these

Answer 1

Answer: (C)

$\frac{255}{1313}$

Answer 2

Let sin B =$\frac{5}{13}$ and sin C =$\frac{99}{101}$, cos B =$\frac{12}{13}$ and

cos C =$\frac{20}{101}$

cos A = cos {180 – (B + C)} = –cos (B + C)

= –(cos B cos C – sin B sin C)

= $\frac{5}{13} \times \frac{99}{101} - \frac{12}{13} \times \frac{20}{101}$= $\frac{255}{1313}$