Question

in the triangle shown, what is the value of sin y°?
note: figure not drawn to scale.
a $\frac{29}{5}$
b $\frac{29}{24}$
c $\frac{24}{29}$
d $\frac{5}{29}$

Explanation:

Step1: Recall the sine formula

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\).

Step2: Identify the sides relative to angle \(y\)

For angle \(y\), the side opposite to \(y\) has length \(24\) (using the Pythagorean theorem \(a = \sqrt{29^{2}-5^{2}}=\sqrt{(29 + 5)(29 - 5)}=\sqrt{34\times24}=\sqrt{676}=24\)), and the hypotenuse has length \(29\).
So, \(\sin y=\frac{24}{29}\)

Answer:

C. \(\frac{24}{29}\)