Question

A triangle has sides with lengths of 10 miles, 12 miles, and 17 miles. Is it a right triangle? yes no

Answer 1

you can solve a triangle if you have the 3 sides

using these formulas

$\begin{gathered} \cos A=\frac{b^2+c^2-a^2}{2bc} \\ \\ \cos B=\frac{a^2+c^2-b^2}{2ac} \end{gathered}$

So

$\begin{gathered} \cos A=\frac{10^2+12^2-17^2}{2(10)(12)} \\ \cos A=\frac{-45}{240} \\ A=\cos ^{-1}(\frac{-45}{240}) \\ A=100.8 \end{gathered}$$undefined$

the sum of all the angles must equal 180

$\begin{gathered} A+B+C=180 \\ 100.8+35.29+C=180 \\ C=180-35.29-100.8 \\ C=43.41 \end{gathered}$

a rigth triangle have an angle of 90°, so this triangle isn't rigth