Answer : c = 31.69 ≈32
Calculations :
GIVEN:
• side b = 24
,
• side a = 16
,
• angle C = 103°
,
• side c = ?
We will use the cosine formula to find the missing side :
[tex]\begin{gathered} c\text{ = }\sqrt[]{(\text{ }a^2}+b^2-2ab\cdot\cos \gamma\text{ ) } \\ \text{ where }\gamma\text{ = }\measuredangle C=\text{103}\degree \end{gathered}[/tex]
Substituting the given paramenter into the formula, we get that c =
[tex]\begin{gathered} c\text{ = }\sqrt[]{16^2+24^2\text{ - 2(16)(24)cos 103}\degree} \\ \text{ = }\sqrt[]{(\text{ 832 -(768 cos 103}\degree}) \\ \text{ = }\sqrt[]{(832\text{ -(-172.76)}} \\ =\text{ }\sqrt[]{(832\text{ +172.76)}} \\ =31.69 \\ \therefore\text{ side c = 31.69 }\approx\text{ 32 } \end{gathered}[/tex]
