Right Triangle Trig: Ratios and Finding Sides

Front

What is 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, and the adjacent side.

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

What is the sine ratio?

Back

The sine ratio is defined as the ratio of the length of the opposite side to the length of the hypotenuse: sin(θ) = opposite/hypotenuse.

Front

What is the cosine ratio?

Back

The cosine ratio is defined as the ratio of the length of the adjacent side to the length of the hypotenuse: cos(θ) = adjacent/hypotenuse.

Front

What is the tangent ratio?

Back

The tangent ratio is defined as the ratio of the length of the opposite side to the length of the adjacent side: tan(θ) = opposite/adjacent.

Front

How can you remember the trigonometric ratios?

Back

You can remember the trigonometric ratios using the mnemonic 'Soh Cah Toa': Soh = Sine = Opposite/Hypotenuse, Cah = Cosine = Adjacent/Hypotenuse, Toa = Tangent = Opposite/Adjacent.

Front

If sin(30°) = 1/2, what is the opposite side if the hypotenuse is 10?

Back

The opposite side is 5 (since 10 * 1/2 = 5).

Front

If cos(60°) = 1/2, what is the adjacent side if the hypotenuse is 8?

Back

The adjacent side is 4 (since 8 * 1/2 = 4).

Front

What is the value of tan(45°)?

Back

The value of tan(45°) is 1.