Basic Trig Ratios

Front

What is the sine ratio in a right triangle?

Back

The sine ratio is defined as the ratio of the length of the opposite side to the length of the hypotenuse. It is expressed as: $$\text{sine} = \frac{\text{opposite}}{\text{hypotenuse}}$$.

Front

What is the cosine ratio in a right triangle?

Back

The cosine ratio is defined as the ratio of the length of the adjacent side to the length of the hypotenuse. It is expressed as: $$\text{cosine} = \frac{\text{adjacent}}{\text{hypotenuse}}$$.

Front

What is the tangent ratio in a right triangle?

Back

The tangent ratio is defined as the ratio of the length of the opposite side to the length of the adjacent side. It is expressed as: $$\text{tangent} = \frac{\text{opposite}}{\text{adjacent}}$$.

Front

What is the hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle.

Front

What is the acronym to remember the trigonometric ratios?

Back

The acronym to remember the definitions of the trig ratios is SOH CAH TOA, which stands for: - SOH: Sine = Opposite / Hypotenuse - CAH: Cosine = Adjacent / Hypotenuse - TOA: Tangent = Opposite / Adjacent.

Front

If the opposite side is 9 and the hypotenuse is 41, what is the sine ratio?

Back

The sine ratio is calculated as: $$\text{sine} = \frac{9}{41}$$.

Front

If the adjacent side is 40 and the hypotenuse is 41, what is the cosine ratio?

Back

The cosine ratio is calculated as: $$\text{cosine} = \frac{40}{41}$$.

Front

If the opposite side is 9 and the adjacent side is 40, what is the tangent ratio?

Back

The tangent ratio is calculated as: $$\text{tangent} = \frac{9}{40}$$.

Front

What is the relationship between the sides of a right triangle according to the Pythagorean theorem?

Back

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b): $$c^2 = a^2 + b^2$$.

Front

What is the value of the hypotenuse if the other two sides are 9 and 40?

Back

Using the Pythagorean theorem: $$c = \sqrt{9^2 + 40^2} = \sqrt{81 + 1600} = \sqrt{1681} = 41$$.