Question

Find the area of the triangle described in Problem 8.

Short answer

The area of the triangle is$13.247$square units.

Step-by-step solution

Step 1. Given Information

The given values are$a=8,b=4,C=70°$.

Step 2. Find Semi Perimeter

• The value of the third side as found in question 8 is $7.62$.
• So, the semiperimeter of the triangle is calculated below.

$\begin{array}{rcl}s& =& \frac{4+8+7.62}{2}\\ & =& \frac{19.62}{2}\\ & =& 9.81\end{array}$

Step 3. Find the Area

The area of a triangle is $A=\sqrt{s(s-a)(s-b)(s-c)}$.

$\begin{array}{rcl}A& =& \sqrt{9.81\times 1.81\times 5.81\times 2.19}\\ & \approx & \sqrt{175.49}\\ & \approx & 13.24\end{array}$