Question

in ∆ abc if sin A =cos B then angle c=?
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Answer 1

Answer:

Step-by-step explanation:

then angle C=90°

we know that if sinA has to be equal to cosB,then A should be equal to 90-B

that is A and B should be complementary

because we know sin(90-Ф)=cosФ or cos(90-Ф)=sinФ

comparing this to sinA=cosB, A=90°-B or reverse that is B=90°-A

so anyway,the sum of A+B=90°

so as ABC is a triangle,the sum of the interior angles in a triangle=180°

so A+B+C=180

substituting the value of (A+B) in the equation

90+C=180 ⇒ C=180-90 = 90°

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