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 diagram with labels x, y, z, w, h, x, y, z 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 to drop-down menu with options: express h in terms of angle y and side y, express h in terms of angle x and side z, express y in terms of angle z and side x then the student should drop-down menu with same options as above next

Explanation:

The Law of Sines proof uses the height \( h \) from \( Y \) to \( XZ \). Step 1 relates \( h \) to \( \angle Z \) and side \( x \) (opposite \( \angle X \)). To equate expressions for \( h \), the next step uses the other right triangle \( XYW \): \( \sin(X) = \frac{h}{z} \), so \( h = z\sin(X) \). This matches "express h in terms of angle X and side z".

Answer:

express h in terms of angle X and side z