Given the dimensions of an isosceles triangle as:
[tex]\begin{gathered} a=c=59ft \\ b=40ft \\ A=C=\text{?} \end{gathered}[/tex]
Sketch showing the isosceles triangle
Applying the Cosine rule to obtain the measure of angle A = C
[tex]\begin{gathered} CosA=\frac{b^2+c^2-a^2}{2bc} \\ \\ CosA=\frac{40^2+59^2-59^2}{2\times40\times59} \\ \\ CosA=\frac{1600^{}+3481^{}-3481^{}}{4720} \\ \\ CosA=\frac{1600^{}}{4720}=0.3390 \\ \\ CosA=0.3390 \\ A=\text{Cos}^{-1}(0.3390) \\ A=70.18^0 \end{gathered}[/tex]
Therefore, A = C = 70.18⁰ (nearest hundredth)
