Step 1: Sum of angle in a triangle =180
[tex]\begin{gathered} 33^0\text{ + 132}^0+l=180^0 \\ l=180^0-165^0 \\ l=25^0 \end{gathered}[/tex]
Step 2: Find the value of m using the sine rule
Sine rule is given as
[tex]\frac{\sin K}{k}=\frac{\sin M}{m}=\frac{\sin L}{l}[/tex]
k= 1.1 inches
K = 33°
M = 136°
L = 25°
After substitution we will have
[tex]\begin{gathered} \frac{\sin33}{1.1}=\frac{\sin136}{m} \\ m\sin 33\text{ = 1.1sin136} \\ 0.54464m=0.76412 \\ m\text{ =1.4inches} \end{gathered}[/tex]
Step 3
Find l using sine rule
[tex]\begin{gathered} \frac{\sin33}{1.1}=\frac{\sin 25\text{ }}{\text{l}} \\ l\sin 33\text{ = 1.1sin25} \\ l=0.854\text{ inches} \end{gathered}[/tex]
Step 4
Find the area of the triangle using heroin's formula stated as
[tex]\begin{gathered} A=\sqrt[]{s(s-a)(s-b)(s-c)_{}} \\ \text{where s, the semiperimeter}=\frac{a+b+c}{2} \end{gathered}[/tex]
Where
a= k =1.1 inches
b = m = 1.4 inches
c = l =0.854 inches
Substituting these in
Hence the area of 0.5 square inches
