Question

in a right angled triangle ABC,given that A is acute and Tan A=5/12, find sin A and cos A​

Answer 1

Given,

In ΔABC,

∠A is an obtuse angle

sin A = 3/5,

=> cos A = -4/5

(°.° A is obtuse, it lies in 2nd quadrant )

and,

sin B = 5/13,

=> cos B = 12/13

To find: sin C

We know that, in a triangle

∠A+∠B+∠C = 180

=> ∠A + ∠B = 180- ∠C

=> sin ( ∠A + ∠B ) = sin ( 180- ∠C )

=> sinA cosB + cosA sinB = sinC

=> sinC = (3/5)(12/13) + (-4/5)(5/13)

=> sin C = 36/65 - 20/65

=> sin C = 16/65