special right triangles

Front

What is a 45°-45°-90° triangle?

Back

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

Front

What is a 30°-60°-90° triangle?

Back

A special right triangle with angles measuring 30°, 60°, and 90°. The ratio of the lengths of the sides opposite these angles is 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 length of the side opposite the 30° angle is 'x', then the side opposite the 60° angle is 'x√3' and the hypotenuse is '2x'.

Front

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

Back

If each leg of the triangle is 'a', then the length of the hypotenuse is 'a√2'.

Front

What is the formula to find the length of the side opposite the 30° angle in a 30°-60°-90° triangle?

Back

The length of the side opposite the 30° angle is half the length of the hypotenuse.

Front

If the hypotenuse of a 30°-60°-90° triangle is 10, what are the lengths of the other two sides?

Back

The side opposite the 30° angle is 5, and the side opposite the 60° angle is 5√3.

Front

In a 45°-45°-90° triangle, if one leg is 7, what is the length of the hypotenuse?

Back

The hypotenuse is 7√2.

Front

What is the Pythagorean theorem?

Back

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

Front

How do you calculate the distance from the base of a ladder to the wall if the ladder forms a 60° angle with the ground?

Back

Use the cosine function: distance = hypotenuse * cos(60°).

Front

If a ladder is 40 ft long and forms a 60° angle with the ground, how far is the base of the ladder from the wall?

Back

The distance is 20 ft.