Question

lemar is completing a proof of the law of sines. his first step is shown. step 1: sin(x) = h/z h = zsin(x) lemar should next use the sine function to define in terms of. then he can to demonstrate the law.

Explanation:

Step1: Recall sine - definition

In right - triangle with angle \(X\), \(\sin(X)=\frac{h}{z}\), so \(h = z\sin(X)\).

Step2: Consider other right - triangle

There is another right - triangle in the big triangle. Let's consider the angle \(Z\). We know that \(\sin(Z)=\frac{h}{x}\), so \(h=x\sin(Z)\).

Step3: Equate the two expressions for \(h\)

Since \(h = z\sin(X)\) and \(h=x\sin(Z)\), we have \(z\sin(X)=x\sin(Z)\), or \(\frac{\sin(X)}{x}=\frac{\sin(Z)}{z}\).

Step4: Generalize for all angles

We can repeat the process for the third angle \(Y\) and get \(\frac{\sin(X)}{x}=\frac{\sin(Y)}{y}=\frac{\sin(Z)}{z}\), which is the law of sines.

Answer:

The learner should next use the sine function for angle \(Z\) to get \(h = x\sin(Z)\), then equate the two expressions for \(h\) to start deriving the law of sines.