Question

Use Pythagoras theorem to determine whether the triangle is acute, obtuse, or right angled-triangle: 6 cm, 8 cm, 11 cm.

Answer 1

Obtuse-Angled Triangle

Step-by-step explanation:

The Pythagorean Theorem is stated below:

`\begin{gathered} c^2=a^2+b^2 \\ c=\text{the hypotenuse which is the longest side} \end{gathered}`

Substitute the given values: 6 cm, 8 cm, 11 cm.

`\begin{gathered} 11^2\stackrel{?}{=}6^2+8^2 \\ 121\stackrel{?}{=}36+64 \\ 121>100 \end{gathered}`

Since we have that:

`c^2>a^2+b^2`

Therefore, we have an obtuse-angled triangle.

Note:

[tex]\begin{gathered} c^2=a^2+b^2\colon\text{Right Triangle} \\ c^2>a^2+b^2\colon\text{Obtuse} \\ c^2