Question

which relationship in the triangle must be true? triangle with right angle at c, sides labeled a (bc), b (ac), hypotenuse c (ab), angles at a, b, c options: sin(b) = sin(a); sin(b) = cos(90 - b); cos(b) = sin(180 - b); cos(b) = cos(a)

Explanation:

Step1: Recall co - function identity

The co - function identity states that \(\sin(x)=\cos(90^{\circ}-x)\) for any acute angle \(x\) in a right - triangle.

Step2: Apply the identity to angle \(B\)

Let \(x = B\). Then, according to the co - function identity \(\sin(B)=\cos(90^{\circ}-B)\)

Answer:

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