Question

A triangle has side lengths 10, 15, and 7. Is the triangle acute, obtuse, or right? please explain.

Answer 1

pythagorean theorem: take the short sides and multiply the squares and compare to the square of the long side to know if the triangle is right, obtuse, acute. If the triangle is a right triangle then according to the pythagorean theorem the squares of the two shorter sides, added together, will equal the square of the hypotenuse.

10 squared (100) plus 7 squared (49) = 149

15 squared = 225

Therefore this triangle is not right. This is an acute triangle because the hypotenuse (is it still a hypotenuse if the triangle is not right?) is shorter than a right triangle's hypotenuse would be.

Answer 2

thank you so much

Answer 3

ur welcome!!

Answer 4

the largest angle is opposite to the largest side so let us check for the largest angle. let it be A.
from cosine rule
cosA=(10^2+7^2-15^2)/2*10*7<0 this implies that A is obtuse therefore it is an obtuse angled triangle.