Chapter 6.1, Problem 4E

To determine

The area of the oblique triangle.

Answer to Problem 4E

The result is $\frac{1}{2}ab\sin C$ .

Explanation of Solution

Given:

The area of the oblique triangle $ABC\text{is }\frac{1}{2}bc\sin A=\frac{1}{2}ab\sin C=$ ........

Since, the area of the oblique is given as:

  $\begin{array}{l}\frac{1}{2}\left(\text{length of two sides}\right)\left(\text{sine of the included angle}\right)\\ \text{Area=}\frac{1}{2}bc\sin A\\ =\frac{1}{2}ac\sin B\\ =\frac{1}{2}ab\sin C\end{array}$

Therefore, the missing term is $\frac{1}{2}ab\sin C$ .