Chapter 3.4, Problem 19WE

To determine

All three angles.

Answer to Problem 19WE

All three angles are, ${30}^0,{60}^0,{90}^0$

Explanation of Solution

Given :

The largest two angle of triangle is two and three times of smallest angle.

Let the smallest angle is x.

Then other two angles will be 2x and 3x.

According to property of triangle sum of angles of a triangle is 180.

Therefore,

  $\begin{array}{l}x+2x+3x={180}^0\\ 6x={180}^0\\ x=\frac{{180}^0}{6}\\ ={30}^0\end{array}$

So the sides of triangle will be,

  $\begin{array}{l}x={30}^0\\ 2x=2\times 30={60}^0\\ 3x=3\times 30={90}^0\end{array}$

Therefore, angle of triangles are ${30}^0,{60}^0,{90}^0$