Lesson 3B Exit 30:60:90 Triangles

Front

What is a 30:60:90 triangle?

Back

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

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'.

Front

Find the length of the hypotenuse if the shortest side is 5.

Back

The hypotenuse is 10, since it is twice the length of the shortest side.

Front

If the hypotenuse of a 30:60:90 triangle is 12, what is the length of the shortest side?

Back

The shortest side is 6, since it is half the length of the hypotenuse.

Front

What is the length of the side opposite the 60° angle if the shortest side is 4?

Back

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

Front

If the side opposite the 30° angle is 3, what is the length of the side opposite the 60° angle?

Back

The length of the side opposite the 60° angle is 3√3.

Front

In a 30:60:90 triangle, if the side opposite the 60° angle is 9, what is the length of the hypotenuse?

Back

The hypotenuse is 18, since it is twice the length of the shortest side.

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) * (shortest side) * (shortest side * √3).

Front

If the side opposite the 30° angle is 5, what is the area of the triangle?

Back

The area is (1/2) * 5 * (5√3) = 12.5√3.

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.