Question

find xy.
triangle with right angle at x, side wx is √39, angle at w is 37°
write your answer as an integer or as a decimal rounded to the nearest tenth.
xy =
submit

Explanation:

Step1: Identify trigonometric ratio

In right triangle \(WXY\), \(\sin W = \frac{XY}{WX}\)

Step2: Substitute known values

\(\sin 37^\circ \approx 0.6\), \(WX = \sqrt{39} \approx 6.245\)

Step3: Calculate XY

\(XY = WX \times \sin W \approx 6.245 \times 0.6 \approx 3.747 \approx 4\)? Wait, no—wait, \(\sin 37^\circ\) is approximately 0.6, but let's use exact? Wait, no, wait: \(\sqrt{39} \times \sin 37^\circ\) is about 6.2450.6=3.747≈3.7≈4? No, wait, maybe \(\sin 37^\circ\) is taken as 0.6 exactly, so 6.2450.6=3.747≈3.7, but the problem says integer or decimal rounded to nearest tenth. Wait, but wait—wait, maybe the triangle uses \(\sin 37^\circ = 3/5\), so let's check: if \(\sin W = XY/WX\), then \(XY = WX \times \sin W = \sqrt{39} \times 3/5 ≈6.245×0.6≈3.747≈3.7\), but maybe the problem expects 3? No, wait, no—wait, maybe I made a mistake. Wait, \(\sqrt{39}\) is about 6.245, times 0.6 is about 3.7, which rounds to 3.7. But let's confirm: 6.245*0.6=3.747, which is 3.7 when rounded to nearest tenth. So the answer is 3.7.

Wait, correct calculation: \(\sqrt{39} ≈6.244998\), multiply by 0.6: 6.244998*0.6=3.7469988≈3.7. So the answer is 3.7.

Step1: Use sine ratio

\(\sin W = \frac{XY}{WX}\)

Step2: Substitute values

\(\sin 37^\circ ≈0.6\), \(WX=\sqrt{39}≈6.245\)

Step3: Compute XY

\(XY≈6.245×0.6≈3.7\)

Answer:

3