Question

The two equal sides of an isosceles triangle are a =C= 59ft. If the base measurement 40 feet,Then A =c

Answer 1

Given the dimensions of an isosceles triangle as:

`\begin{gathered} a=c=59ft \\ b=40ft \\ A=C=\text{?} \end{gathered}`

Sketch showing the isosceles triangle

Applying the Cosine rule to obtain the measure of angle A = C

`\begin{gathered} CosA=(b^2+c^2-a^2)/(2bc) \\ \\ CosA=(40^2+59^2-59^2)/(2*40*59) \\ \\ 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}`

Therefore, A = C = 70.18⁰ (nearest hundredth)