Question

Solve the triangle. B = 72°, b = 12, c = 8

Answer 1

The answer is 12^2=x^2+8^2-16x(cos(72°) 
x^2-4.9443x=80 
(x-2.4721)^2=86.1115 
x-2.4721=±9.2796 
x=11.7517 

B=72°, b=12, c=8, a=11.8 
C=arcsin(8/12*sin(72°))=39.3° 
A=68.7° 

Answer 2

Answer:

Part 1) $C=39.3\°$

Part 2) $A=68.7\°$

Part 3) $a=11.8\ units$

Step-by-step explanation:

we know that

Applying the law of sines

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

In this problem we have

$B=72\°$

$b=12\ units$

$c=8\ units$

Step 1

Find the measure angle C

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

substitute the values and solve for C

$\frac{12}{sin(72\°)} =\frac{8}{sin(C)}\\ \\sin(C)=sin(72\°)*(8/12)\\ \\sin(C)= 0.6340\\ \\C=39.3\°$

Step 2

Find the measure of angle A

we know that

The sum of the internal angles of the triangle must be equal to $180$ degrees

so

$m$

we have

$m$

$m$

$m$

$m$

Step 3

Find the measure of side a

Applying the law of cosines

$a^{2}=b^{2}+c^{2}-2(b)(c)cos(A)$

substitute

$a^{2}=12^{2}+8^{2}-2(12)(8)cos(68.7\°)$

$a^{2}=208-(192)cos(68.7\°)$

$a^{2}=138.26$

$a=11.8\ units$