2024 UPDATED!!! Solve the triangle. a = 32°, a = 19, b = 14

THIS USER ASKED 👇

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

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

Step by step explanation:

We have both sides of a triangle and we have an angle.

A = 32 °, a = 19, b = 14

We use the older theorem for angle B.

We know it to be true by these theorems:

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

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

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

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

So:

$C = 180-32-22.98 \\ C = 125.02 °$

Eventually we find the side c

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

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

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

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