Question

Classify the triangle based on side lengths 5, 7 and 8.
A. right
B. Acute
C. obtuse
D. no triangle can be formed with given side lengths

Answer 1

This can be done by using the pythagorean theorem, but changing the equal sign to an inequality, which we do not know the sign yet.
First, take the two smaller lengths and plug them in for a and b of the pythagorean theorem:
a^2+b^2(?)c^2
5^2+7^2(?)c^2
Now instead of solving for c, you plug the largest side in for c and simplify the two sides:
5^2+7^2(?)8^2
25+49(?)64
74(?)64
Now at this point if the number of the smaller two sides (a and b) is larger than the hypotenuse alone, then it is an acute triangle. If the a and b side is smaller than the hypotenuse alone, then it is an obtuse triangle, and, of course, if they are equal, then it is a right triangle.

Answer 2

Hope this helped! If you need any more information don't hesitate to ask.

Answer 3

i need more info

Answer 4

wouldnt it be obtuse

Answer 5

So plug the two smaller sides into the pythagorean theorem for a and b, then plug the hypotenuse in for c.
Acute example:
5^2+7^2(?)8^2
25+49(?)64
74≥64
The left side is larger, so this is acute.
Right example:
5^2+12^2(?)13^2
25+144(?)169
169=169
Both sides are the same, so this is a right triangle.
Obtuse example:
5^2+6^2(?)12^2
25+36(?)144
61≤144
The right side is larger, so this is obtuse.

Answer 6

so the answer is C obtuse