Chapter 8.2, Problem 64AYU

To determine

How to solve a triangle when one side and two angles are given?

Answer to Problem 64AYU

We will get all the information about the triangle by using law of Sine

Explanation of Solution

Given information:

What do you do first if you are asked to solve a triangle and are given one side and two angles?

Calculation:

Let us consider an oblique triangle having the side $a$ , $b$ and $c$ with respect to the opposite angles $A$ , $B$ and $C$ in which one side and two angles are given. Now, you should follow the following steps.

Apply the property of the triangle

  $A+B+C=180°\mathrm{.....}\left(1\right)$

And find the third unknown angle.

Apply low of Sine

  $\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}\mathrm{.....}\left(2\right)$

In which angle A, B, C and one sides amongst a, b, c is given say a,

Take first two in $\left(2\right)$ , you will get

  $\frac{\sin A}{a}=\frac{\sin B}{b}$

  $b=a\times \frac{\sin B}{\sin A}\mathrm{.....}\left(3\right)$

Take first and last in $\left(2\right)$ , you will get

  $\frac{\sin A}{a}=\frac{\sin C}{c}$

  $c=a\times \frac{\sin C}{\sin A}\mathrm{.....}\left(4\right)$

Hence, we will get all the information about the triangle by using law of Sine in this case.