Trig Ratios and Special Right Triangles

Front

What is a 45-45-90 triangle?

Back

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

Front

What is the ratio of the sides in a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the ratio of the lengths of the sides is 1:√3:2, where 1 is the length of the short leg, √3 is the length of the longer leg, and 2 is the length of the hypotenuse.

Front

What does 'Soh Cah Toa' stand for?

Back

It is a mnemonic to remember the definitions of sine, cosine, and tangent: Soh = Sine = Opposite/Hypotenuse, Cah = Cosine = Adjacent/Hypotenuse, Toa = Tangent = Opposite/Adjacent.

Front

How do you find the hypotenuse in a 30-60-90 triangle if the short leg is known?

Back

Multiply the length of the short leg by 2 to find the hypotenuse.

Front

What is the sine of an angle?

Back

The sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse (Opp/Hyp).

Front

What is the cosine of an angle?

Back

The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse (Adj/Hyp).

Front

What is the tangent of an angle?

Back

The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side (Opp/Adj).

Front

What is the relationship between the legs in a 45-45-90 triangle?

Back

The lengths of the legs are equal, and the hypotenuse is √2 times the length of each leg.

Front

If the hypotenuse of a 30-60-90 triangle is 10, what is the length of the short leg?

Back

The length of the short leg is 10/2 = 5.

Front

What is the formula to find the length of the longer leg in a 30-60-90 triangle?

Back

Multiply the length of the short leg by √3 to find the longer leg.