Chapter 8.4, Problem 3ST1

a.

To determine

To check:Triangle is acute, obtuse or right.

Answer to Problem 3ST1

Right-angled triangle

Explanation of Solution

Given information: sides have dimensions $11,60,61$

Let $a,b,c$ denote sides of the triangle.

If $a^2+b^2=c^2$ then the triangle is said to be right angled triangle.

Take $a=11,b=60,c=61$

  $\begin{array}{l}{a}^2+b^2={11}^2+{60}^2=121+3600=3721\\ c^2={61}^2=3721\\ \Rightarrow a^2+b^2=c^2\end{array}$

So, triangle with sides of dimensions $11,60,61$ is a right-angled triangle.

b.

To determine

To check: The given triangle is acute angled, obtuse angled or right angled triangle

Answer to Problem 3ST1

Acute triangle

Explanation of Solution

Given information: sides have dimensions $7,9,11$

Let $a,b,c$ denote sides of the triangle.

If $a^2+b^2>c^2$ then the triangle is acute

Take $a=7,b=9,c=11$

  $\begin{array}{l}{a}^2+b^2=7^2+9^2=49+81=130\\ c^2={11}^2=121\\ \Rightarrow a^2+b^2>c^2\end{array}$

So, triangle with sides of dimensions $7,9,11$ is acute

c.

To determine

To check:The triangle is acute, obtuse or right.

Answer to Problem 3ST1

Right-angled triangle

Explanation of Solution

Given information: sides have dimensions $0.2,0.3,0.4$

Let $a,b,c$ denote sides of the triangle.

If $a^2+b^2<c^2$ then the triangle is obtuse

Take $a=0.2,b=0.3,c=0.4$

  $\begin{array}{l}{a}^2+b^2={0.2}^2+{0.3}^2=0.04+0.09=0.13\\ c^2={0.4}^2=0.16\\ \Rightarrow a^2+b^2<c^2\end{array}$

So, triangle with sides of dimensions $0.2,0.3,0.4$ is obtuse