Question

1. determine the length of xy to the nearest tenth of a centimetre.

a. 36.9 cm
b. 41.4 cm
c. 8.5 cm
d. 16.8 cm

Explanation:

Step1: Identify the trigonometric relation

In right - triangle $XYZ$ with right - angle at $Y$, we know the hypotenuse $XZ = 17.4$ cm and the angle $\angle Z=61^{\circ}$, and we want to find the side $XY$. We use the sine function since $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\sin Z=\frac{XY}{XZ}$.

Step2: Rearrange the formula to solve for $XY$

We can rewrite the formula as $XY = XZ\times\sin Z$.

Step3: Substitute the given values

We know that $XZ = 17.4$ cm and $Z = 61^{\circ}$. So, $XY=17.4\times\sin(61^{\circ})$.
Since $\sin(61^{\circ})\approx0.8746$, then $XY = 17.4\times0.8746\approx15.2$ cm.

Answer:

b. $15.2$ cm