Question

Which relationship in the triangle must be true? Triangle A B C is shown. Angle A C B is a right angle. The length of side C B is a, the length of side A C is b, and the length of side A B is c. Sin(B) = sin(A) sin(B) = cos(90 – B) cos(B) = sin(180 – B) cos(B) = cos(A)

Answer 1

Answer:

b

sin(b)=cos(90-b)

Step-by-step explanation:

Answer 2

Answer:

sin(B) = cos(90 – B)

Step-by-step explanation:

In a right triangle, there are specific trigonometric relations called trigonometric reasons. In any right triangle like it's shown in the image attached, we have:

$sinB=\frac{b}{c}$

Now, the angle $90-B$ is actually equal to angle $A$, because angles $A$ and $B$ are complementary, they sum 90°. So, we have: $90-B=A$.

Then, from trigonometric reasons we have:

$cosA=\frac{b}{c}$

But, $cosA=cos(90-B)$

So,

$sinB=\frac{b}{c}=cosA=cos(90-B)$

Hence, $sinB=cos(90-B)$