Question

14
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 correctly started the proof.
the next step in the proof is t
then the student should

Explanation:

Step1: Analyze the start of the proof

In a right - triangle (formed by height \(h\), side \(x\) and part of the base), using the sine function \(\sin(Z)=\frac{h}{x}\) (sine of an angle in a right - triangle is opposite over hypotenuse) and then \(x\sin(Z) = h\) is a correct start.

Step2: Find the next step

We also have another right - triangle with angle \(X\), hypotenuse \(z\) and height \(h\). Using the sine function \(\sin(X)=\frac{h}{z}\), then \(z\sin(X)=h\). Since we already have \(x\sin(Z) = h\) and \(z\sin(X)=h\), we can set \(x\sin(Z)=z\sin(X)\) (because both equal \(h\)). So the next step is to express \(h\) in terms of angle \(X\) and side \(z\).

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 \(z\).