Question

Given a triangle with a =14 A = 41 and B = 34, what is the length of c? Round to the nearest tenth

Answer 1

Answer:

20.6°

Step-by-step explanation:

Given in a triangle

a = 14 ∠A = 41° and ∠B = 34°

Then we have to find the measure of side c

Since sum of all angles of a triangle is 180°

So   ∠A + ∠B + ∠C = 180°

       41° +  34° + ∠C = 180°

        75° + ∠C = 180°

         ∠C = 180 - 75

               = 105°

Now from sine rule,

$\frac{a}{SinA}= \frac{c}{SinC}$

$\frac{14}{Sin(41)}= \frac{c}{Sin(105)}$

$c=\frac{14\times Sin(105)}{Sin(41)}$

$c=\frac{14\times 0.9659}{0.6561}$

= 20.61°

≈ 20.6°

Answer 2

Your answer is 20.6