the sines of two angles of a triangle are equal to `5/13 & 99/101` the cosine of the third angle is

Options

A. `255//1313`
B. `265//1313`
C. `275//1313`
D. `770//1313`

Answer

A

Explanation

Let `sintheta=(5)/(13)andsinphi=(99)/(101)`
`thereforecos{pi-(theta+phi)}`
`=-cos(theta+phi)`
`=-{costhetacosphi-sinthetasinphi}`
`=-{sqrt(1-(25)/(169))sqrt(1-((99)/(101))^(2))-(5)/(13)xx(99)/(101)}`
`=-{(12)/(13)xx(20)/(101)-(5)/(13)xx(99)/(101)}`
`=-{(240)/(1313)-(495)/(1313)}=(255)/(1313)`