Trigonometric Ratios and Right Triangles

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

Define sine (sin) in a right triangle.

Back

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

Front

Define cosine (cos) in a right triangle.

Back

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

Front

Define tangent (tan) in a right triangle.

Back

Tangent (tan) is the ratio of the length of the opposite side to the length of 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

How do you find the length of the hypotenuse using trigonometric ratios?

Back

To find the hypotenuse, use the formula: hypotenuse = opposite / sin(angle) or hypotenuse = adjacent / cos(angle).

Front

What is the relationship between the angles and sides in a right triangle?

Back

The angles in a right triangle determine the ratios of the lengths of the sides, which are consistent for similar triangles.

Front

How do you calculate the height of an object using trigonometric ratios?

Back

Height can be calculated using the formula: height = distance * tan(angle).

Front

What is the Law of Sines?

Back

The Law of Sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant for all three sides of the triangle.

Front

What is the Law of Cosines?

Back

The Law of Cosines relates the lengths of the sides of a triangle to the cosine of one of its angles: c² = a² + b² - 2ab*cos(C).