Question

The lengths of the sides of the triangle are 3, 8, and 10. Is the triangle a right triangle, acute triangle, or an obtuse triangle?

Answer 1

Answer:

Obtuse

Step-by-step explanation:

1. You have to make sure it is a triangle by adding the smallest and the medium sides, if the result is greater than the bigger side then it is a triangle.
2. you then use the Pythagorean theorem to check if the triangle is a right triangle, acute, or obtuse. If $c^{2}$ = $a^{2} +b^{2}$ then it is a right triangle. If $c^{2} >a^{2} + b^{2}$ then it is an obtuse triangle. if $c^{2} < a^{2} +b^{2}$ then it is an acute triangle.

1. $10^{2}$ _ $3^{2} + 8^{2}$
2. 9+64_100
3. 70_100
4. 70<100

in this case $c^{2}$ is greater than $a^{2} +b^{2}$ therefore, is it an obtuse triangle.