Question

question 2(multiple choice worth 4 points)
(05 02 lc)
the figure below shows a right triangle.
what is r/q equal to?
o tan x°
o sin y°
o sin x°
o tan y°

Explanation:

Step1: Recall trigonometric ratio definitions

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\), \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\).
For angle \(x^{\circ}\), \(\sin x^{\circ}=\frac{p}{q}\), \(\tan x^{\circ}=\frac{p}{r}\).
For angle \(y^{\circ}\), \(\sin y^{\circ}=\frac{r}{q}\), \(\tan y^{\circ}=\frac{r}{p}\).
We want to find the value of \(\frac{r}{q}\).

Step2: Match with trigonometric ratio

Since \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\), and for angle \(y^{\circ}\), the opposite side is \(r\) and the hypotenuse is \(q\).

Answer:

\(\sin y^{\circ}\)