obtuse or acute and why

okay, here we go

You need to use a special version of the pythagorean theorum

15^2 _ 10^2 + 12^2

225 _ 100 + 144

225 _ 244

since 225 is less than 244, it is an obtuse triangle

best represents a triangle with the lengths 10in., 12in., 15in.,

Sorry YaraYugi you had the right idea but you got a bit confused. :)

In any triangle the longest side is opposit the biggest angle.

And we want to know if the biggest angle is greater or less than 90 degrees

so I will call the short sides a and b and the long side c

a=10, b=12 and    c=15

If

\(a^2+b^2>c^2 \qquad \text{Then angle C is acute}\\ a^2+b^2=c^2 \qquad \text{Then angle C is a right angled}\\ a^2+b^2<c^2 \qquad \text{Then angle C is obtuse}\\ \)

 10^2+12^2 = 244

15^2=225

244>225 so Angle C is acute

This is an acute angled triangle.

Here is the triangle drawn to scale