Special Right Triangles

Front

What is a 45-45-90 triangle?

Back

A 45-45-90 triangle is an isosceles right triangle where the angles are 45°, 45°, and 90°. The lengths of the legs are equal, and the length of the hypotenuse is √2 times the length of each leg.

Tags

CCSS.8.G.B.8

Front

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

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2. The side opposite the 30° angle is the shortest, the side opposite the 60° angle is √3 times the shortest side, and the hypotenuse is twice the shortest side.

Tags

CCSS.HSG.CO.C.10

Front

How do you find the length of the hypotenuse in a 45-45-90 triangle?

Back

To find the length of the hypotenuse in a 45-45-90 triangle, multiply the length of one leg by √2.

Tags

CCSS.8.G.B.8

Front

How do you find the length of the longer leg in a 30-60-90 triangle?

Back

To find the length of the longer leg in a 30-60-90 triangle, multiply the length of the shorter leg (opposite the 30° angle) by √3.

Tags

CCSS.8.G.B.8

Front

What is the formula for the area of a triangle?

Back

The area of a triangle can be calculated using the formula: Area = 1/2 * base * height.

Tags

CCSS.6.G.A.1

Front

What is the Pythagorean theorem?

Back

The Pythagorean theorem states that 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.

Tags

CCSS.8.G.B.7

Front

What is the value of x in a 45-45-90 triangle if each leg is 4?

Back

If each leg is 4, then the hypotenuse x is 4√2.

Tags

CCSS.8.G.B.8

Front

What is the value of the hypotenuse in a 30-60-90 triangle if the shorter leg is 5?

Back

If the shorter leg is 5, then the hypotenuse is 10.

Tags

CCSS.8.G.B.8

Front

What type of triangle has angles of 30°, 60°, and 90°?

Back

A triangle with angles of 30°, 60°, and 90° is called a 30-60-90 triangle.

Tags

CCSS.4.G.A.2

Front

What is the length of the shorter leg in a 30-60-90 triangle if the hypotenuse is 12?

Back

If the hypotenuse is 12, the shorter leg (opposite the 30° angle) is 6.

Tags

CCSS.8.G.B.8