Question

select the correct answer from each drop - down menu.
a student began a proof of the law of sines using triangle xyz. his work is shown.

step 1: \\( \sin ( z ) = \frac { h } { x } \\)
\\( x \sin ( z ) = h \\)
the student has started the proof.
the next step in the proof is to.
then the student shou use the law of cosines use the tangent function set the expressions for h equal

Explanation:

Step1: Analyze the first part

In the right - triangle formed with side \(x\) (hypotenuse) and height \(h\), using the sine function \(\sin(Z)=\frac{h}{x}\) (opposite over hypotenuse) is correct. So the student has correctly started the proof.

Step2: Analyze the second part

In the right - triangle formed with side \(z\) (hypotenuse) and height \(h\), we can write \(\sin(X)=\frac{h}{z}\), then \(h = z\sin(X)\). Since we already have \(h=x\sin(Z)\) from Step 1.

Step3: Set the two expressions for \(h\) equal

Set \(z\sin(X)=x\sin(Z)\), which is a key step in proving the Law of Sines \(\frac{\sin(X)}{x}=\frac{\sin(Z)}{z}\)

Answer:

The student has correctly started the proof. The next step in the proof is to express \(h\) in terms of angle \(X\) and side \(z\). Then the student should set the expressions for \(h\) equal.