Triangle Trigonometry Basics

Front

What is the definition of a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

Front

What does SOH-CAH-TOA stand for?

Back

SOH-CAH-TOA is a mnemonic for remembering the definitions of the sine, cosine, and tangent functions: Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent.

Front

What is the sine of an angle in a right triangle?

Back

The sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse.

Front

What is the cosine of an angle in a right triangle?

Back

The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse.

Front

What is the tangent of an angle in a right triangle?

Back

The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.

Front

How do you find the length of a side in a right triangle using trigonometric ratios?

Back

You can use the sine, cosine, or tangent ratios depending on which sides and angles you know.

Front

What is the Pythagorean theorem?

Back

The Pythagorean theorem states that 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

If the opposite side is 10 cm and the hypotenuse is 20 cm, what is the sine of the angle?

Back

Sine = Opposite/Hypotenuse = 10/20 = 0.5.

Front

If the adjacent side is 15 cm and the hypotenuse is 25 cm, what is the cosine of the angle?

Back

Cosine = Adjacent/Hypotenuse = 15/25 = 0.6.

Front

If the opposite side is 8 cm and the adjacent side is 6 cm, what is the tangent of the angle?

Back

Tangent = Opposite/Adjacent = 8/6 = 1.33.