Respuesta :

34 ^2 + 28^2 = 42^2

Work out both sides of the equation. If they do not equal then it is not a right triangle. If I remember correctly it is obtuse if the right is larger and acute if the left is bigger.

Right angled triangle is the triangle with its one of the angles with 90 degrees. The considered triangle is Obtuse triangle.

How are triangles discriminated based on angles?

  • If all of three angles of a triangle are < 90° then triangle is acute.
  • If one of the angle is of 90°  then the triangle is right angled triangle.
  • If one of the angle is  > 90°  then triangle is called obtuse triangle.

How to identify if a triangle is acute, right angled or obtuse?

Let we have:

  • H = biggest side of the triangle
  • And let we get  A and B as rest of the two sides.

Then we get:

  • If [tex]A^2 + B^2 < H^2[/tex], then triangle is acute
  • If [tex]A^2 + B^2 = H^2[/tex], then triangle is right angled triangle
  • If [tex]A^2 + B^2 > H^2[/tex], then triangle is obtuse.


For the given case, the triangle considered has 3 sides of lengths 34 inches, 28 inches, and 42 inches.

Longest side is of 42 inches, thus, H = 42 inches

Then, Let A = 34 inches and B = 28 inches (order doesn't matter between A and B)

Then, evaluating their squares and sum of squares of A and B, we get:

[tex]A^2 + B^2 = 34^2 + 28^2 = 1940\\H^2 = 42^2 = 1764\\Thus,\\\\A^2 + B^2 > H^2[/tex]

Thus, triangle is obtuse.

Learn more about acute, right angled and obtuse triangles here:

https://brainly.com/question/1401739