Chapter 12.9, Problem 1OE

To determine

Find the formula for area of triangle ABC such that $\angle A=25°,\angle B=50°\text{ and }b=30$ .

Answer to Problem 1OE

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

Explanation of Solution

Given information: The given triangle ABC has $\angle A=25°,\angle B=50°\text{ and }b=30$ .

Calculation: Since the given triangle ABC has $\angle A=25°,\angle B=50°\text{ and }b=30$ . And the given triangle has case the case of angle-angle-side where the side is non included side between the given two angles. Therefore the formula for area $\left(A\right)$ of triangle ABC is written as,

  $A=\frac{1}{2}{b}^2\left(\frac{\sin A\sin C}{\sin B}\right)$