Looking at the right triangle, choose THREE statements that are true.

Question

The image depicts a right-angled triangle labeled ABC, with angle C being the right angle. Side a (BC) is labeled as 8, the hypotenuse c (AB) is labeled as 10, and angle A is given as 53.13°. This is a classic example used in trigonometry to illustrate the relationships between angles and sides in a right triangle.

(3 points)
Responses

Right triangles must have the side across from the 90 degree angle as the longest side.
Right triangles must have the side across from the 90 degree angle as the longest side.

Right triangles have interior angles that add to equal 180 degrees.
Right triangles have interior angles that add to equal 180 degrees.

Right triangles have side lengths that are always rational numbers.
Right triangles have side lengths that are always rational numbers.

Right triangles have interior angles that are all acute angles.
Right triangles have interior angles that are all acute angles.

Right triangles have the pattern that the sum of the two shorter sides = the longest side.
Right triangles have the pattern that the sum of the two shorter sides = the longest side.

Right triangles have side lengths that always follow a2+b2=c2
Right triangles have side lengths that always follow A squared plus b squared is equal to c squared

Answer 1

Based on the characteristics of right triangles, the following three statements are true:

1. Right triangles must have the side across from the 90-degree angle as the longest side.
   This is a fundamental property of right triangles, where the hypotenuse (the longest side) is opposite the right angle.

2. Right triangles have interior angles that add to equal 180 degrees.
   This is true for all triangles, including right triangles, as the sum of the interior angles in any triangle is always 180 degrees.

3. Right triangles have side lengths that always follow \(a^2 + b^2 = c^2\).
   This statement refers to the Pythagorean theorem, which is a defining property of right triangles, stating that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

The other statements are not true:

• Right triangles do not need to have side lengths that are always rational numbers.
• Right triangles do not have all angles that are acute (one angle is always 90 degrees).
• The sum of the two shorter sides does not equal the longest side; rather, it’s the sum of the squares of the two shorter sides that equals the square of the longest side.

Therefore, the correct answers are the first, second, and sixth statements.