Special Triangle Mrs. G

Front

What is a 45-45-90 triangle?

Back

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

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, where 1 is the length of the side opposite the 30° angle, √3 is opposite the 60° angle, and 2 is the hypotenuse.

Front

How do you find the length of the hypotenuse in a right triangle?

Back

Use the Pythagorean theorem: a² + b² = c², where c is the hypotenuse and a and b are the other two sides.

Front

What is the Pythagorean theorem?

Back

A mathematical principle stating that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Front

If one leg of a 45-45-90 triangle is 5, what is the length of the hypotenuse?

Back

5√2.

Front

What is the formula to find the area of a triangle?

Back

Area = 1/2 * base * height.

Front

In a 45-45-90 triangle, if one leg is x, what is the length of the other leg?

Back

The length of the other leg is also x.

Front

What is the length of the legs in a 30-60-90 triangle if the shortest leg is 4?

Back

The lengths are 4 (shortest leg), 4√3 (longer leg), and 8 (hypotenuse).

Front

How do you determine if three lengths can form a triangle?

Back

Use the triangle inequality theorem: the sum of the lengths of any two sides must be greater than the length of the third side.

Front

What is the length of y in a 45-45-90 triangle if one leg is 8?

Back

8.