Question

Solve triangle ABC if A = 65°, B = 65°, and c = 6. If no triangle exists, explain why.

Answer 1

Part 1)
`m\angle C=50^o`

Part 2)
`a=7.1\ units`

Part 3)
`b=7.1\ units`

Explanation:

step 1

Find the measure of angle C

we know that

The sum of the interior angles in any triangle must be equal to 180 degrees

`m\angle A+m\angle B+m\angle C=180^o`

substitute the given values

`65^o+65^o+m\angle C=180^o`

`130^o+m\angle C=180^o`

`m\angle C=180^o-130^o`

`m\angle C=50^o`

step 2

Find the measure of side a

Applying the law of sines

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

substitute the given values

`(a)/(sin(65^o))=(6)/(sin(50^o))`

solve for a

`a=(6)/(sin(50^o))sin(65^o)`

`a=7.1\ units`

step 3

Find the measure of side b

Applying the law of sines

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

substitute the given values

`(b)/(sin(65^o))=(6)/(sin(50^o))`

solve for b

`b=(6)/(sin(50^o))sin(65^o)`

`b=7.1\ units`

The triangle ABC is an isosceles triangle