Chapter 8, Problem 9CT

To determine

Todetermine:The area of the triangle having lengths of two sides as $a=8$, $b=4$ and an angle $C={70}^0$ .

Answer to Problem 9CT

Solution:

The area of the given triangle is $5.4723\text{square units}$ .

Explanation of Solution

Given information:

The triangle having $a=8$, $b=4$ ,and $C={70}^0$ .

In the triangle $a=8$, $b=4$, and $C={70}^0$ ,two sides and one angle is given.Hence use “Area of an SAS triangle” formula to find the area of the given triangle.

The formula to find area of SAS triangle is $K=\frac{1}{2}ab\sin C$ .

Plug the values $a=8$, $b=4$ and $C={70}^0$ in the above formula.

Thus, $K=\frac{1}{2}\cdot 8\cdot 4\cdot \sin {70}^{°}$ .

  $\Rightarrow K=16\left(0.3420\right)=15.0350$ .

Therefore, the area of the given triangle is $15.0350$ square units.