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

Question

asked Jan 6, 2020 2.7k views

1 Answer

Ice · Answer 1 · 2020-01-12T23:50:27+0000

Answer:

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