Question

Find the area of the triangle with the given measurements. Round the solution to the nearest hundredth if necessary.

B = 107°, a = 10 cm, c = 22 cm.

A. 32.16 cm^2
B. 110 cm^2
C. 105.19 cm^2
210.39 cm^2

Answer 1

Check the picture below.

now, we have a triangle with all three sides, thus we can use Heron's Area Formula on the triangle.

`\bf \qquad \textit{Heron's area formula} \\\\ A=√(s(s-a)(s-b)(s-c))\qquad \begin{cases} s=(a+b+c)/(2)\\[-0.5em] \hrulefill\\ a=10\\ b=26.695\\ c=22\\ s=29.3475 \end{cases} \\\\\\ A=√(29.3475(29.3475-10)(29.3475-26.695)(29.3475-22)) \\\\\\ A=√(29.3475(19.3475)(2.6525)(7.3475))\implies A\approx √(11066.007) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill A\approx 105.195~\hfill`