Special Right Triangles

Front

What is a 30-60-90 triangle?

Back

A special right triangle where the angles measure 30 degrees, 60 degrees, and 90 degrees. The sides are in the ratio 1:√3:2.

Front

What are the side lengths of a 30-60-90 triangle if the shortest side is 6?

Back

The side lengths are 6 (shortest), 6√3 (longer leg), and 12 (hypotenuse).

Front

What is the Pythagorean theorem?

Back

In a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): c² = a² + b².

Front

How can you determine if a triangle is acute, obtuse, or right using side lengths?

Back

Use the Pythagorean theorem: If a² + b² > c², it's acute; if a² + b² < c², it's obtuse; if a² + b² = c², it's right.

Front

What are the conditions for three lengths to form a triangle?

Back

The sum of the lengths of any two sides must be greater than the length of the third side.

Front

Given sides 4, 6, and 7, what type of triangle is formed?

Back

Acute triangle.

Front

Given sides 28, 45, and 53, what type of triangle is formed?

Back

Right triangle.

Front

Can the sides of a triangle be 4, 7, and 18?

Back

No, because 4 + 7 is not greater than 18.

Front

What is the ratio of the sides in a 45-45-90 triangle?

Back

The sides are in the ratio 1:1:√2.

Front

What is a 45-45-90 triangle?

Back

A special right triangle where the angles are both 45 degrees and the sides opposite these angles are equal.