Question

Solve ABC
c=10, B=35°, C=65%​

Answer 1

Part 1) The measure of angle A is
`A=80\°`

Part 2) The length side of a is equal to
`a=10.9\ units`

Part 3) The length side of b is equal to
`b=6.3\ units`

Explanation:

step 1

Find the measure of angle A

we know that

The sum of the internal angles of a triangle must be equal to 180 degrees

so

`A+B+C=180\°`

substitute the given values

`A+35\°+65\°=180\°`

`A+100\°=180\°`

`A=180\°-100\°=80\°`

step 2

Find the length of side a

Applying the law of sines

`(a)/(sin(A))=(c)/(sin(C))`

substitute the given values

`(a)/(sin(80\°))=(10)/(sin(65\°))`

`a=(10)/(sin(65\°))(sin(80\°))`

`a=10.9\ units`

step 3

Find the length of side b

Applying the law of sines

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

substitute the given values

`(b)/(sin(35\°))=(10)/(sin(65\°))`

`b=(10)/(sin(65\°))(sin(35\°))`

`b=6.3\ units`