Question

Find C Find A and find ab=21 c=26 B=34 degrees

Answer 1

The Law of Sines states that:

$\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}$

Procedure

0. Using the Law of Sines to ,find C

$\frac{\sin B}{b}=\frac{\sin C}{c}$

As we have the values of all variables but C, we isolate for it:

$\sin C=\frac{\sin B}{b}$

$C=\sin ^{-1}(\frac{\sin B}{b}\cdot c)$

Replacing the values:

$C=\sin ^{-1}(\frac{\sin34}{21}\cdot26)$

$C=\sin ^{-1}(0.6923)$

$C=43.82$

2. Calculating A

Then, knowing that all the interior angles of a triangle add up to 180°...

$A+B+C=180$

...we can isolate for A:

$A=180-B-C$

Replacing the values given for B and the value of C:

$A=180-34-43.82$

$A=102.18$

3. Calculating a

Now that we know A, we can find a using the Law of Sines:

$\frac{\sin A}{a}=\frac{\sin B}{b}$

Isolating for a we get:

$a=\frac{\sin A}{\frac{\sin B}{b}}$

Replacing the values:

$a=\frac{\sin 102.18}{\frac{\sin 34}{21}}$

$a=36.71$

Answer:

• C = 43.82°

,

• A = 102.18°

,

• a = 36.71