Question

which is the approximate measure of angle y? use the law of sines to find the answer. law of sines: $\frac{sin(a)}{a}=\frac{sin(b)}{b}=\frac{sin(c)}{c}$

Explanation:

Step1: Identify the sides and angles for law of sines

Let $x = 2.7$, $y=2.8$, and $\angle Z = 63^{\circ}$. By the law of sines, $\frac{\sin(Y)}{x}=\frac{\sin(Z)}{y}$.

Step2: Substitute the values

We have $\sin(Y)=\frac{x\sin(Z)}{y}$. Substituting $x = 2.7$, $y = 2.8$, and $\sin(Z)=\sin(63^{\circ})\approx0.891$, we get $\sin(Y)=\frac{2.7\times0.891}{2.8}$.

Step3: Calculate $\sin(Y)$

$\sin(Y)=\frac{2.7\times0.891}{2.8}=\frac{2.4057}{2.8}\approx0.8592$.

Step4: Find the angle $Y$

$Y=\sin^{- 1}(0.8592)\approx59^{\circ}$.

Answer:

$59^{\circ}$