Chapter 1.7, Problem 9PSB

To determine

Whether $\Delta ABC$ is acute angle Triangle or not.

Answer to Problem 9PSB

No, $\Delta {\rm A}{\rm B}C$ is not acute angle triangle.

Explanation of Solution

Given Information: Angle $A$

  $$ and $B$ are acute in $\Delta {\rm A}{\rm B}C$ .

Formula Used:The sum of all the angle of the triangle is ${180}^o$$\angle A+\text{}\angle B+\text{}\angle C={180}^o$

Proof: Any triangle is said to be acute angle triangle, if all three angles are acute.

If any of the angle is not acute, then triangle would not be acute. Therefore, if two angles are acute, then it is not necessary that third angle would be acute.

For e.g. In $\Delta {\rm A}{\rm B}C$ , $\angle A=60°$ , $\angle B=20°$

Then from the triangle property (sum of all the angle of the triangle is ${180}^o$ ), the third angle would be

  $\begin{array}{l}\angle A+\text{}\angle B+\text{}\angle C={180}^o\\ {60}^o+{20}^o+\angle C={180}^o\\ \angle C={100}^o\end{array}$

Hence, $\angle C$ is not acute because it is more than ${90}^o$ , therefore the $\Delta ABC$ would not be acute.