Solve using the law of sines and a scaled drawing. Round to the nearest tenth. If two triangles exist, solve both completely. side b = 20.0 mi
$\angle$B = 51°
Side a = 21.6 mi
A) A $\approx$ 57.1°, C $\approx$ 71.9°
C $\approx$24.5 mi
B) A $\approx$122.9° C $\approx$ 6.1°
C $\approx$ 2.7 mi
C) A $\approx$ 57.1° C $\approx$ 71.9°
C $\approx$24.5 mi
Or
A $\approx$ 122.9°
C $\approx$6.1°
C $\approx$ 2.7 mi
D) not possible

Question

Quizplus · Accepted Answer

Using the law of sines, we have:

$\frac{\sin 51°}{20.0} = \frac{\sin A}{21.6}$

Solving for A, we get $A \approx 57.1°$.

Then, using the fact that the three angles of a triangle add up to 180°, we have:

$C = 180° - A - 51° \approx 71.9°$

Finally, using the law of sines again, we can solve for side c:

$\frac{\sin C}{c} = \frac{\sin 51°}{20.0}$

$c \approx 24.5$ mi

Therefore, choice C is the best answer. The other choices either have incorrect angle measures or result in non-real solutions.

Solve Using the Law of Sines and a Scaled Drawing ∠\angle∠

Solve Using the Law of Sines and a Scaled Drawing $\angle$