Question

In ΔABC, ∠A is an obtuse angle. If sin A = 3/5, sin B = 5/13, find sin C.​

Answer 1

$Answer:</p><p>{sin C = \frac{16}{65}}sinC=6516</p><p>Step-by-step explanation:</p><p>Given,</p><p>In ΔABC,</p><p>∠A is an obtuse angle</p><p>sin A = 3/5,</p><p>=> cos A = -4/5</p><p>(°.° A is obtuse, it lies in 2nd quadrant )</p><p>and,</p><p>sin B = 5/13,</p><p>=> cos B = 12/13</p><p>To find: sin C</p><p>We know that, in a triangle</p><p>∠A+∠B+∠C = 180</p><p>=> ∠A + ∠B = 180- ∠C</p><p>=> sin ( ∠A + ∠B ) = sin ( 180- ∠C )</p><p>=> sinA cosB + cosA sinB = sinC</p><p>=> sinC = (3/5)(12/13) + (-4/5)(5/13)</p><p>=> sin C = 36/65 - 20/65</p><p>=> sin C = 16/65</p><p>$

Answer 2

Given:sinA=hypotenuseoppositeside=53

⇒adjacentside=(hypotenuse)2−(oppositeside)2

=52−32=25−9=16=4

⇒cosA=hypotenuseadjacentside=54

∴sinA=53,cosA=54

Given:sinB=hypotenuseoppositeside=135

⇒adjacentside=(hypotenuse)2