30-60-90 and 45-45-90 Triangles

Front

What is a 30-60-90 triangle?

Back

A right triangle where the angles are 30 degrees, 60 degrees, and 90 degrees. The sides are in the ratio 1 : √3 : 2.

Front

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

Back

If the short leg is 'x', then the longer leg is 'x√3' and the hypotenuse is '2x'.

Front

Find the longer leg if the short leg of a 30-60-90 triangle is 9.

Back

9√3

Front

What is a 45-45-90 triangle?

Back

A right triangle where the angles are both 45 degrees and the sides opposite these angles are equal.

Front

What is the relationship between the sides of a 45-45-90 triangle?

Back

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

Front

Find the hypotenuse if each leg of a 45-45-90 triangle is 7 cm.

Back

7√2 cm

Front

How do you simplify the expression 8√3?

Back

It is already in its simplest form.

Front

What is the value of 'a' and 'b' in a 45-45-90 triangle if a = 5√2 and b = 5√2?

Back

Both legs are equal, each measuring 5√2.

Front

If the hypotenuse of a 30-60-90 triangle is 18, what is the length of the short leg?

Back

9 (since the hypotenuse is 2 times the short leg).

Front

What is the formula to find the hypotenuse in a 45-45-90 triangle?

Back

Hypotenuse = leg × √2.