Chapter 12.9, Problem 2OE

To determine

Find the formula for area of triangle ABC such that $a=18,b=10\text{ and }\angle C=45°$ .

Answer to Problem 2OE

The formula for area $\left(A\right)$ of triangle ABC is $A=\frac{1}{2}ab\sin C$ .

Explanation of Solution

Given information: The given triangle ABC has $a=18,b=10\text{ and }\angle C=45°$ .

Calculation: Since the given triangle ABC has $a=18,b=10\text{ and }\angle C=45°$ . And the given triangle has the case of side-angle-side where the given angle $\left(\angle C=45°\right)$ is included angle between the given two sides $a=18\text{ and }b=10$ . Therefore the formula for area $\left(A\right)$ of triangle ABC is written as,

  $A=\frac{1}{2}ab\sin C$