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.
triangle xyz with a perpendicular from y to xz, meeting at w, labeled with sides x, y, z, and height h
step 1: $sin(z)=\frac{h}{x}$
$xsin(z)=h$
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 dropdown with options: use the law of cosines, set the expressions for h equal, use the tangent function
reset and next buttons

Explanation:

Step1: Confirm first expression for h

Student found \( h = x\sin(Z) \) from right triangle YWZ.

Step2: Get second expression for h

Next, \( \sin(X) = \frac{h}{z} \Rightarrow h = z\sin(X) \) from right triangle YWX.

Step3: Equate the two h expressions

To derive Law of Sines, set \( x\sin(Z) = z\sin(X) \Rightarrow \frac{x}{\sin(X)} = \frac{z}{\sin(Z)} \). Thus, the next step is to set the expressions for h equal.

Answer:

set the expressions for h equal