Chapter 8.4, Problem 56AYU

To determine

To state: The area of an SAS triangle in words.

Answer to Problem 56AYU

The area of an SAS triangle in words is explained below.

Explanation of Solution

Given:

The three sides is given.

Calculation:

If side of a triangle is a , base of a triangleis b are given, and an angel, C between a and b, is given then $\sin C=\frac{h}{a}$ if $b$ is the base of triangle and $h$ is the height of the triangle.

The above formula can be arranged into $h=a\sin C$ .

As it is known that area of a Parallelogram is $A=\text{base}\times h$ and the area of SAS triangle is $A=\frac{1}{2}\times \text{Area}\text{of}\text{Parallelogram}$ . So,

  $\begin{array}{c}\text{Area}\text{of}\text{triangle}=\frac{1}{2}\times \text{base}\times h\\ =\frac{1}{2}\times b\times a\sin C\\ =\frac{1}{2}\times ab\sin C\end{array}$