Question

which is the approximate measure of angle y? use the law of sines to find the answer. 52° 59° 64° 67° law of sines: \\(\frac{\sin(a)}{a} = \frac{\sin(b)}{b} = \frac{\sin(c)}{c}\\) triangle with vertices x, y, z: xz = 2.7, xy = 2.8, angle at z is 63°

Explanation:

Step1: Apply the law of sines

The law of sines states that \(\frac{\sin(X)}{x}=\frac{\sin(Y)}{y}=\frac{\sin(Z)}{z}\). Here, \(y = 2.7\), \(z=2.8\), and \(Z = 63^{\circ}\). So, \(\frac{\sin(Y)}{2.7}=\frac{\sin(63^{\circ})}{2.8}\).

Step2: Solve for \(\sin(Y)\)

Cross - multiply: \(\sin(Y)=\frac{2.7\times\sin(63^{\circ})}{2.8}\). We know that \(\sin(63^{\circ})\approx0.891\). Then \(\sin(Y)=\frac{2.7\times0.891}{2.8}=\frac{2.4057}{2.8}\approx0.859\).

Step3: Find the angle \(Y\)

Take the inverse - sine of \(0.859\). \(Y=\sin^{- 1}(0.859)\approx59^{\circ}\).

Answer:

\(59^{\circ}\)