30-60-90 Special Right Triangles Practice

Front

What is a 30-60-90 triangle?

Back

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

Tags

CCSS.HSG.CO.C.10

Front

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

Back

In a 30-60-90 triangle, if the shortest side (opposite the 30° angle) is 'x', then the side opposite the 60° angle is 'x√3', and the hypotenuse (opposite the 90° angle) is '2x'.

Tags

CCSS.HSG.CO.C.10

Front

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

Back

To find the hypotenuse, double the length of the shortest side (opposite the 30° angle). If the shortest side is 'x', then the hypotenuse is '2x'.

Tags

CCSS.8.G.B.8

Front

If the shortest side of a 30-60-90 triangle is 5, what is the length of the hypotenuse?

Back

The hypotenuse is 10, since it is double the shortest side (5).

Tags

CCSS.HSG.CO.C.10

Front

What is the value of the side opposite the 60° angle in a 30-60-90 triangle if the shortest side is 4?

Back

The side opposite the 60° angle is 4√3.

Tags

CCSS.8.G.B.8

Front

What is the formula to find the area of a 30-60-90 triangle?

Back

The area can be calculated using the formula: Area = (1/2) * base * height. For a 30-60-90 triangle, Area = (1/2) * x * (x√3) = (x^2√3)/2.

Tags

CCSS.6.G.A.1

Front

What is the value of x in a 30-60-90 triangle if the hypotenuse is 12?

Back

If the hypotenuse is 12, then x (the shortest side) is 6, since the hypotenuse is 2x.

Tags

CCSS.8.G.B.8

Front

If the side opposite the 60° angle is 9√3, what is the length of the shortest side?

Back

The shortest side is 9, since the side opposite the 60° angle is x√3.

Tags

CCSS.HSG.SRT.C.8

Front

What is the Pythagorean theorem?

Back

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b): c² = a² + b².

Tags

CCSS.8.G.B.8

Front

How can the Pythagorean theorem be applied to a 30-60-90 triangle?

Back

In a 30-60-90 triangle, you can use the Pythagorean theorem to verify the relationship between the sides: (2x)² = x² + (x√3)².

Tags

CCSS.8.G.B.8