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:

$\begin{gathered} \angle B=74^{\circ} \\ a=14\operatorname{cm} \\ c=20\operatorname{cm} \end{gathered}$

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:

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

Therefore, the area f