Question

spiral review • assessment readiness
find the value of y.
which of the following is the correct response?
show hints
2.4
3.7
4.0
19.5

Explanation:

Step1: Recall the sine - law formula

The sine - law states that in a triangle $\triangle XYZ$, $\frac{\sin X}{x}=\frac{\sin Y}{y}=\frac{\sin Z}{z}$. First, find the measure of angle $Z$. Since the sum of angles in a triangle is $180^{\circ}$, $Z = 180^{\circ}-(80.2^{\circ}+35.8^{\circ})=64^{\circ}$.

Step2: Apply the sine - law

We know that $\frac{\sin Y}{y}=\frac{\sin Z}{z}$. Given $Y = 35.8^{\circ}$, $Z = 64^{\circ}$, and $z = 4.1$. So, $\frac{\sin35.8^{\circ}}{y}=\frac{\sin64^{\circ}}{4.1}$. Cross - multiply to get $y\times\sin64^{\circ}=4.1\times\sin35.8^{\circ}$. Then $y=\frac{4.1\times\sin35.8^{\circ}}{\sin64^{\circ}}$.

Step3: Calculate the value of $y$

We know that $\sin35.8^{\circ}\approx0.585$ and $\sin64^{\circ}\approx0.899$. Then $y=\frac{4.1\times0.585}{0.899}=\frac{2.3985}{0.899}\approx2.4$.

Answer:

2.4