Question

State if each triangle is acute, obtuse,or right using Pythagorean theorem converse.

Answer 1

Right triangle

Explanation:

Properties for acute, obtuse or right triangle,

1). Given triangle will be a right triangle if,

Hypotenuse² = (Leg 1)² + (Leg 2)²

2). Triangle will be an acute triangle if,

(Largest side)² < (leg 1)² + (leg 2)²

3). Triangle will be an obtuse triangle if,

(Largest side)² > (leg 1)² + (leg 2)²

Now we apply these properties in the given triangle,

(Largest side)² = (√11105)²

= 11105

(leg 1)² = (76)²

= 5776

(leg 2)² = (73)²

= 5329

Since 11105 = 5776 + 5329 (First Property)

11105 = 11105

Therefore, given triangle is a right triangle.