Question

question: 8
a right triangle is shown below.
which of the following equals sin a?
a tan a
b. cos b
c. tan b
d. cos a

Explanation:

Step1: Recall trigonometric ratio definitions

In a right - triangle \(ABC\) with \(\angle C = 90^{\circ}\), \(\sin A=\frac{\text{opposite}}{\text{hypotenuse}}=\frac{a}{c}\), \(\cos B=\frac{\text{adjacent}}{\text{hypotenuse}}\).
For \(\angle B\), the adjacent side is \(a\) and the hypotenuse is \(c\). So, \(\cos B=\frac{a}{c}\).

Step2: Compare the values

Since \(\sin A=\frac{a}{c}\) and \(\cos B = \frac{a}{c}\).

Answer:

B. \(\cos B\)