First, use the Law of Sines to find the measurement of angle \(\displaystyle B.\)

\(\displaystyle \frac{12}{\sin 21}=\frac{16}{\sin B}\)

\(\displaystyle 12\sin B = 5.73\)

\(\displaystyle \sin B=0.48\)

\(\displaystyle B= 28.69\)

Recall that all the angles in a triangle need to add up to \(\displaystyle 180\) degrees.

\(\displaystyle 21+28.69+A=180\)

\(\displaystyle A=130.31\)

Now, use the Law of Sines again to find the length of \(\displaystyle d\).

\(\displaystyle \frac{d}{\sin 130.31}=\frac{12}{\sin 21}\)

\(\displaystyle d \sin 21= 9.15\)

\(\displaystyle d=25.53\)

First, use the Law of Sines to find the measurement of angle \(\displaystyle B.\)

\(\displaystyle \frac{6}{\sin34}=\frac{9}{\sin B}\)

\(\displaystyle 6 \sin B = 5.03\)

\(\displaystyle \sin B=0.84\)

\(\displaystyle B= 57.14\)

Recall that all the angles in a triangle need to add up to \(\displaystyle 180\) degrees.

\(\displaystyle 34+57.14+A=180\)

\(\displaystyle A=88.86\)

Now, use the Law of Sines again to find the length of \(\displaystyle d\).

\(\displaystyle \frac{d}{\sin 88.86}=\frac{6}{\sin 34}\)

\(\displaystyle d \sin 34=5.9988\)

\(\displaystyle d=10.73\)

First, use the Law of Sines to find the measurement of angle \(\displaystyle B.\)

\(\displaystyle \frac{13}{\sin 54}=\frac{14}{\sin B}\)

\(\displaystyle 13\sin B = 11.33\)

\(\displaystyle \sin B=0.87\)

\(\displaystyle B= 60.46\)

Recall that all the angles in a triangle need to add up to \(\displaystyle 180\) degrees.

\(\displaystyle 54+60.46+C=180\)

\(\displaystyle C=65.54\)

Now, use the Law of Sines again to find the length of \(\displaystyle d\).

\(\displaystyle \frac{d}{\sin 65.54}=\frac{13}{\sin 54}\)

\(\displaystyle d \sin 54= 11.83\)

\(\displaystyle d=14.63\)

First, use the Law of Sines to find the measurement of angle \(\displaystyle B.\)

\(\displaystyle \frac{6}{\sin 41}=\frac{8}{\sin B}\)

\(\displaystyle 6\sin B = 5.25\)

\(\displaystyle \sin B=0.875\)

\(\displaystyle B= 61.04\)

Recall that all the angles in a triangle need to add up to \(\displaystyle 180\) degrees.

\(\displaystyle 41+61.04+C=180\)

\(\displaystyle C=77.96\)

Now, use the Law of Sines again to find the length of \(\displaystyle d\).

\(\displaystyle \frac{d}{\sin 77.96}=\frac{6}{\sin 41}\)

\(\displaystyle d \sin 41= 5.87\)

\(\displaystyle d=8.95\)

First, use the Law of Sines to find the measurement of angle \(\displaystyle B.\)

\(\displaystyle \frac{9}{\sin 35}=\frac{12}{\sin B}\)

\(\displaystyle 9\sin B = 6.88\)

\(\displaystyle \sin B=0.76\)

\(\displaystyle B= 49.46\)

Recall that all the angles in a triangle need to add up to \(\displaystyle 180\) degrees.

\(\displaystyle 35+49.46+C=180\)

\(\displaystyle C=95.54\)

Now, use the Law of Sines again to find the length of \(\displaystyle d\).

\(\displaystyle \frac{d}{\sin 95.54}=\frac{9}{\sin 35}\)

\(\displaystyle d \sin 35= 8.96\)

\(\displaystyle d=15.62\)

First, use the Law of Sines to find the measurement of angle \(\displaystyle C.\)

\(\displaystyle \frac{17}{\sin 33}=\frac{16}{\sin C}\)

\(\displaystyle 17\sin C = 8.71\)

\(\displaystyle \sin C= 0.51\)

\(\displaystyle C= 30.66\)

Recall that all the angles in a triangle need to add up to \(\displaystyle 180\) degrees.

\(\displaystyle 33+30.66+B=180\)

\(\displaystyle B=116.34\)

Now, use the Law of Sines again to find the length of \(\displaystyle d\).

\(\displaystyle \frac{d}{\sin 116.34}=\frac{17}{\sin 33}\)

\(\displaystyle d \sin 33= 15.24\)

\(\displaystyle d=27.98\)

First, use the Law of Sines to find the measurement of angle \(\displaystyle C.\)

\(\displaystyle \frac{19}{\sin 37}=\frac{24}{\sin C}\)

\(\displaystyle 19\sin C = 14.44\)

\(\displaystyle \sin C= 0.76\)

\(\displaystyle C= 49.46\)

Recall that all the angles in a triangle need to add up to \(\displaystyle 180\) degrees.

\(\displaystyle 37+49.46+B=180\)

\(\displaystyle B=93.54\)

Now, use the Law of Sines again to find the length of \(\displaystyle d\).

\(\displaystyle \frac{d}{\sin 93.54}=\frac{19}{\sin 37}\)

\(\displaystyle d \sin 37 = 18.96\)

\(\displaystyle d=31.50\)

First, use the Law of Sines to find the measurement of angle \(\displaystyle C.\)

\(\displaystyle \frac{7}{\sin 29}=\frac{4}{\sin C}\)

\(\displaystyle 7\sin C = 1.94\)

\(\displaystyle \sin C= 0.28\)

\(\displaystyle C= 16.26\)

Recall that all the angles in a triangle need to add up to \(\displaystyle 180\) degrees.

\(\displaystyle 16.26+29+B=180\)

\(\displaystyle B=134.74\)

Now, use the Law of Sines again to find the length of \(\displaystyle d\).

\(\displaystyle \frac{d}{\sin 134.74}=\frac{7}{\sin 29}\)

\(\displaystyle d \sin 29= 4.97\)

\(\displaystyle d=10.25\)

First, use the Law of Sines to find the measurement of angle \(\displaystyle B.\)

\(\displaystyle \frac{19}{\sin 61}=\frac{20}{\sin B}\)

\(\displaystyle 19\sin B = 17.49\)

\(\displaystyle \sin B=0.92\)

\(\displaystyle B= 66.93\)

Recall that all the angles in a triangle need to add up to \(\displaystyle 180\) degrees.

\(\displaystyle 61+66.93+C=180\)

\(\displaystyle C=52.07\)

Now, use the Law of Sines again to find the length of \(\displaystyle d\).

\(\displaystyle \frac{d}{\sin 52.07}=\frac{19}{\sin 61}\)

\(\displaystyle d \sin 61= 14.99\)

\(\displaystyle d=17.14\)

First, use the Law of Sines to find the measurement of angle \(\displaystyle B.\)

\(\displaystyle \frac{13}{\sin 64}=\frac{9}{\sin C}\)

\(\displaystyle 13\sin C = 8.09\)

\(\displaystyle \sin C=0.62\)

\(\displaystyle C= 38.32\)

Recall that all the angles in a triangle need to add up to \(\displaystyle 180\) degrees.

\(\displaystyle 64+38.32+B=180\)

\(\displaystyle B=77.68\)

Now, use the Law of Sines again to find the length of \(\displaystyle d\).

\(\displaystyle \frac{d}{\sin 77.68}=\frac{13}{\sin 64}\)

\(\displaystyle d \sin 64= 12.70\)

\(\displaystyle d=14.13\)