Question

I really need help. My math teacher doesn't want to help me and isn't responding to my emails. Could you explain how to solve each of these? Thank you so much!!!

Answer 1

4. To determine if a triangle is a right triangle, given that you know the length of its sides, you have to check if its lengths follow the Pythagorean theorem.

This theorem states that the square of the hypothenuse (c) is equal to the sum of the squares of the legs of the triangle (a and b), following the expression:

`a^2+b^2=c^2`

The triangle is:

We have to check that a²+ b² is equal to c².

The square of the hypothenuse is:

`\begin{gathered} c^2=10^2 \\ c^2=100 \end{gathered}`

The sum of the squares of the legs of the triangle is:

`\begin{gathered} a^2+b^2=8^2+6^2 \\ a^2+b^2=64+36 \\ a^2+b^2=100 \end{gathered}`

As you can see, the sum of the squares of the legs of the triangle is 100, which is the same as the square of the hypothenuse. The triangle follows the Pythagorean theorem and can be considered a right triangle.