Trig Ratios in Right Triangles

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 are the three sides of a right triangle called?

Back

The three sides are called the hypotenuse (the longest side), the opposite side (opposite the angle), and the adjacent side (next to the angle).

Front

What is the sine ratio in a right triangle?

Back

Sine (sin) of an angle is the ratio of the length of the opposite side to the length of the hypotenuse.

Front

What is the cosine ratio in a right triangle?

Back

Cosine (cos) of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse.

Front

What is the tangent ratio in a right triangle?

Back

Tangent (tan) of an angle is the ratio of the length of the opposite side to the length of the adjacent side.

Front

How can you remember the trigonometric ratios?

Back

Use the mnemonic 'Soh Cah Toa': Soh = Sin = Opposite/Hypotenuse, Cah = Cos = Adjacent/Hypotenuse, Toa = Tan = Opposite/Adjacent.

Front

If sin(θ) = 0.5, what is θ?

Back

θ = 30° or θ = 150°.

Front

What is the Pythagorean theorem?

Back

In a right triangle, a² + b² = c², where c is the hypotenuse and a and b are the other two sides.

Front

If the opposite side is 10 and the hypotenuse is 20, what is sin(θ)?

Back

sin(θ) = 10/20 = 0.5.

Front

If cos(θ) = 0.6, what is the adjacent side if the hypotenuse is 10?

Back

Adjacent side = cos(θ) * hypotenuse = 0.6 * 10 = 6.