Identify Trig Ratios

Front

What is a trigonometric ratio?

Back

A trigonometric ratio is a ratio of the lengths of two sides of a right triangle. The primary trigonometric ratios are sine, cosine, and tangent.

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 side opposite the angle 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 side opposite the angle to the length of the adjacent side.

Front

How do you find the length of the opposite side using the sine ratio?

Back

To find the length of the opposite side, multiply the hypotenuse by the sine of the angle: opposite = hypotenuse * sin(angle).

Front

How do you find the length of the adjacent side using the cosine ratio?

Back

To find the length of the adjacent side, multiply the hypotenuse by the cosine of the angle: adjacent = hypotenuse * cos(angle).

Front

How do you find the length of the hypotenuse using the sine ratio?

Back

To find the length of the hypotenuse, divide the length of the opposite side by the sine of the angle: hypotenuse = opposite / sin(angle).

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 relationship between the angles and sides in a right triangle?

Back

In a right triangle, the angles determine the ratios of the sides, and these ratios are consistent for similar triangles.

Front

What is the length of the hypotenuse if the opposite side is 16 and the angle is 30 degrees?

Back

Using the sine ratio: hypotenuse = opposite / sin(30°) = 16 / 0.5 = 32.