Question

Solve the triangle. A = 32°, a = 19, b = 14

Answer 1

Answer:

A = 32°, a = 19, b = 14, B=22.98°, C = 125.02°, c = 29.36

Step-by-step explanation:

We have two sides of the triangle and we have an angle.

A = 32 °, a = 19, b = 14

We use the sine theorem to find the angle B.

We know that according to the sine theorem it is true that:

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

$\frac{sin(32\°)}{19}=\frac{sin(B)}{14}$

$sin(B)=14*\frac{sin(32\°)}{19}\\\\B=Arcsin(14*\frac{sin(32\°)}{19})\\\\B=22.98\°$

We know that the sum of the internal angles of a triangle is always equal to 180.

So:

$C=180-32-22.98\\\\C=125.02\°$

Finally we find the c side

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

$\frac{sin(32\°)}{19}=\frac{sin(125.02)}{c}$

$0.02789=\frac{sin(125.02)}{c}$

$c=\frac{sin(125.02)}{0.02789}\\\\c=29.36$