Special Right Triangles

What is a 45°-45°-90° triangle?

• A triangle with angles of 30°, 60°, and 90°.

• A special right triangle where the angles are 45°, 45°, and 90°. The sides opposite the 45° angles are equal, and the length of the hypotenuse is @@\text{leg} \times \sqrt{2}@@.

• A triangle where all sides are equal in length.

• A triangle with one angle measuring 90° and the other two angles measuring 45° and 45°.

If the shorter leg of a 30°-60°-90° triangle is x, what is the length of the longer leg?

• @@x@@

• @@x + 1@@

• @@x ext{√3}@@

• @@2x@@

What type of triangle is formed by the angles 45°, 45°, and 90°?

• Equilateral triangle

• Isosceles triangle

• 45°-45°-90° triangle

• Scalene triangle

What is a 30°-60°-90° triangle?

• A special right triangle where the angles are 30°, 60°, and 90°. The ratio of the lengths of the sides is 1 : @@ ext{√3}@@ : 2.

• A triangle with angles measuring 30°, 30°, and 120°.

• A triangle where all sides are equal in length.

• A right triangle with angles measuring 45°, 45°, and 90°.

What is the sum of the angles in any triangle?

• 90°

• 180°

• 360°

• 270°

If the leg of a 45°-45°-90° triangle is 10, what is the length of the hypotenuse?

• 10

• 10√2

• 20

• 5√2

In a 30°-60°-90° triangle, if the hypotenuse is 12, what is the length of the longer leg?

• 6√3

• 6

• 12

• 4√3

In a 30°-60°-90° triangle, if the shorter leg is 4, what is the length of the longer leg?

• 4√3

• 4

• 8

• 2√3

If the hypotenuse of a 30°-60°-90° triangle is 10, what is the length of the shorter leg?

• 3

• 4

• 5

• 6

What is the relationship between the sides of a 30°-60°-90° triangle?

• 1 : @@\sqrt{3}@@ : 2 (1 is the shorter leg, @@\sqrt{3}@@ is the longer leg, and 2 is the hypotenuse)

• 1 : 1 : 1 (all sides are equal)

• 1 : 2 : 3 (the sides are in a different ratio)

• 2 : @@\sqrt{3}@@ : 1 (the hypotenuse is the shortest side)