Question

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

Answer 1

The Law of Sines states that:

`(\sin A)/(a)=(\sin B)/(b)=(\sin C)/(c)`

Procedure

0. Using the Law of Sines to ,find C

`(\sin B)/(b)=(\sin C)/(c)`

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

`\sin C=(\sin B)/(b)`

`C=\sin ^(-1)((\sin B)/(b)\cdot c)`

Replacing the values:

`C=\sin ^(-1)((\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:

`(\sin A)/(a)=(\sin B)/(b)`

Isolating for a we get:

`a=(\sin A)/((\sin B)/(b))`

Replacing the values:

`a=(\sin 102.18)/((\sin 34)/(21))`

`a=36.71`

Answer:

• C = 43.82°

,

• A = 102.18°

,

• a = 36.71