Acute or Obtuse?

Part of the Triangles section of Coddy's Geometry journey. Lesson 35 of 63.

The test says more than right or not. Compare the two shorter squares added with the longest square. If they are equal, the angle facing the longest side is 90°. If the sum is bigger, that angle is less than 90°, and the triangle is acute. If the sum is smaller, the angle is more than 90°, and the triangle is obtuse.

Picture a right triangle and swing its two legs apart: the angle between them opens past 90°, and the far side grows longer than the hypotenuse was. Its square then beats the two leg squares together. Close the legs and it shrinks below.

$Three triangles labelled 4, 5, 6 and 3, 5, 7 and 5, 12, 13$

For 4, 5, 6: 16 + 25 = 41 is more than 36, so acute. For 3, 5, 7: 9 + 25 = 34 is less than 49, so obtuse.

Challenge

Each triangle has its three side lengths written on it. Test each one with the squares of its sides, then tap the obtuse triangle and press Check.

Try it yourself

$Find the right part on the figure$