How do you solve the triangle given ∠A = 55°, ∠B = 64°, c = 34?

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Answer 1 · 2017-01-09T21:19:27

Subtract the two known angles from $180^{\circ}$ $180^@$ to find $∠ C$ $angle C$
Use The Law of Sines to compute sides "a" and "b"

Subtract the two known angles from $180^{\circ}$ $180^@$ to find $∠ C$ $angle C$

$∠ C = 180^{\circ} - 55^{\circ} - 64^{\circ} = 61^{\circ}$ $angle C = 180^@ - 55^@ - 64^@ = 61^@$

Use The Law of Sines to compute sides "a" and "b":

$a = c \frac{sin (A)}{sin (C)}$ $a = csin(A)/sin(C)$

$a = 34 \frac{sin (55^{\circ})}{sin (61^{\circ})}$ $a = 34sin(55^@)/sin(61^@)$

$a \approx 31.84$ $a ~~ 31.84$

$b = c \frac{sin (B)}{sin (C)}$ $b = csin(B)/sin(C)$

$b = 34 \frac{sin (64^{\circ})}{sin (61^{\circ})}$ $b = 34sin(64^@)/sin(61^@)$

$b \approx 34.94$ $b ~~ 34.94$