Question

Find the area of the triangle with the given measurements. Round the solution to thenearest hundredth if necessary.B = 74º, a = 14 cm, c = 20 cm (5 points)

Answer 1

Let's begin by listing out the given information:

We will calculate the area as shown below:

`\begin{gathered} \text{We will obtain the third side using the Cosine Rule:} \\ b^2=a^2+c^2-2ac\cdot cosB \\ b=\sqrt[]{a^2+c^2-2ac\cdot cosB} \\ b=\sqrt[]{14^2+20^2-2(14)(20)\cdot cos74^(\circ)} \\ b=21.02cm \end{gathered}`

The formula for area is given by Heron's formula:

`\begin{gathered} A=\sqrt[]{s(s-a)(s-b)(s-c)} \\ s=(a+b+c)/(2)=(14+21.02+20)/(2)=(55.02)/(2)=27.51 \\ s=27.51 \\ \Rightarrow A=\sqrt[]{27.51(27.51-14)(27.51-21.02)(27.51-20)} \\ A=134.58cm^2 \end{gathered}`

Therefore, the area f