Question

which relationship in the triangle must be true? a b c c a b o sin(b) = sin(a) o sin(b) = cos(90 - b) o cos(b) = sin(180 - b) o cos(b) = cos(a)

Explanation:

Step1: Recall co - function identity

The co - function identity states that $\sin\theta=\cos(90^{\circ}-\theta)$ for any angle $\theta$. In a right - triangle $ABC$ with right angle at $C$, for angle $B$, we have this identity.

Step2: Analyze other options

• Option 1: $\sin(B)=\sin(A)$ is not true in general. In right - triangle $ABC$ with right angle at $C$, $\sin(A)=\frac{a}{c}$ and $\sin(B)=\frac{b}{c}$, and $a

eq b$ usually.

• Option 3: $\cos(B)=\sin(180 - B)$. We know that $\sin(180 - B)=\sin B$ and $\cos B

eq\sin B$ in general.

• Option 4: $\cos(B)=\cos(A)$ is not true in general. $\cos(A)=\frac{b}{c}$ and $\cos(B)=\frac{a}{c}$, and $a

eq b$ usually.

Answer:

$\sin(B)=\cos(90 - B)$