# Triangle ADEF is a Right triangle, where angle F =

Triangle ADEF is a Right triangle, where angle F = 90", side d = 19, side f = 38. Find the measure of angle D. Use knowledge of triangles and/or trigonometry to justify your answer.
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skullsxtest7xt
Step 1
in $\mathrm{△}DEF$
$m\mathrm{\angle }F=90°$
d=19
j=38
Use sine law in $\mathrm{△}DEF:$
$\frac{\mathrm{sin}\left(D\right)}{d}=\frac{\mathrm{sin}\left(F\right)}{f}$
$\frac{\mathrm{sin}\left(D\right)}{19}=\frac{\mathrm{sin}\left({90}^{\circ }\right)}{38}$
$\mathrm{sin}\left(D\right)=\frac{19}{38}$
$\mathrm{sin}\left(D\right)=\frac{1}{2}$
$m\mathrm{\angle }D={\mathrm{sin}}^{-1}\left(\frac{1}{2}\right)={30}^{\circ }$
Step 2
$m\mathrm{\angle }D={30}^{\circ }$