Question

which expression is equivalent to \\( \sin 49 ^ { \circ } \\) in the right triangle shown?
choose 1 answer:
\\( \cos \angle c \\)
\\( \sin \angle c \\)
\\( \cos \angle a \\)

Explanation:

Step1: Use the co - function identity

In a right - triangle, \(\sin\theta=\cos(90^{\circ}-\theta)\).
Since \(\theta = 49^{\circ}\), then \(\sin49^{\circ}=\cos(90^{\circ}-49^{\circ})=\cos41^{\circ}\).
In a right - triangle \(ABC\) with \(\angle B = 90^{\circ}\), \(\angle A+\angle C=90^{\circ}\). Given \(\angle A = 49^{\circ}\), then \(\angle C=41^{\circ}\).

Answer:

A. \(\cos\angle C\)