Question

Classify the triangles as ACUTE, OBTUSE, OR RIGHT:(show all work on paper)

Answer 1

Step 1:

In this question, we are given the following:

Step 2:

The details of the solution are as follows:

Let us begin with the second one:

Using Pythagors' theorem, we have that:

`\begin{gathered} c^2=a^2+b^2\text{ } \\ where\text{ a = 30, b = 16 , c = 34} \\ 34^2\text{ = 30}^2+\text{ 16}^2 \\ 1156\text{ = 900 + 256 \lparen correct \rparen} \\ \text{This is a Right -angle Triangle} \end{gathered}`

Step 2:

Back to the first one:

`\begin{gathered} Using\text{ the formulae:} \\ c^{2\text{ }}=a^2+\text{ b}^2\text{ \lparen Right-angle\rparen} \\ c^2\text{ > a}^2+\text{ b}^2\text{ \lparen Obtuse\rparen} \\ c^2\text{ < a}^2+\text{ b}^2\text{ \lparen Acute \rparen} \end{gathered}`

`\begin{gathered} where\text{ c = 24, a = 16 , b = 12} \\ c^2\text{ = 24 x 24 = 576} \\ a^2=\text{ 16 x 16 = 256} \\ b^2=\text{ 12 x 12 = 144} \\ So,\text{ we can see that:} \\ c^2\text{ > a}^2\text{+ b}^2 \\ 576\text{ > 256 + 144} \\ 576\text{ > 400 } \\ Hence,\text{ this is an obtuse triangle} \end{gathered}`