Question

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

Answer 1

Answer:

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

Part 2) $a=7.1\ units$

Part 3) $b=7.1\ units$

Step-by-step 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

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

substitute the given values

$\frac{a}{sin(65^o)}=\frac{6}{sin(50^o)}$

solve for a

$a=\frac{6}{sin(50^o)}sin(65^o)$

$a=7.1\ units$

step 3

Find the measure of side b

Applying the law of sines

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

substitute the given values

$\frac{b}{sin(65^o)}=\frac{6}{sin(50^o)}$

solve for b

$b=\frac{6}{sin(50^o)}sin(65^o)$

$b=7.1\ units$

The triangle ABC is an isosceles triangle