8.2 - Trig - Finding Sides

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 is the Pythagorean theorem?

Back

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): c² = a² + b².

Front

What is the sine function?

Back

The sine function (sin) is a trigonometric function defined as the ratio of the length of the opposite side to the length of the hypotenuse in a right triangle.

Front

What is the cosine function?

Back

The cosine function (cos) is a trigonometric function defined as the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle.

Front

What is the tangent function?

Back

The tangent function (tan) is a trigonometric function defined as the ratio of the length of the opposite side to the length of the adjacent side in a right triangle.

Front

If the opposite side is 10 and the hypotenuse is 20, what is the sine of the angle?

Back

sin(θ) = opposite/hypotenuse = 10/20 = 0.5.

Front

If the adjacent side is 15 and the hypotenuse is 25, what is the cosine of the angle?

Back

cos(θ) = adjacent/hypotenuse = 15/25 = 0.6.

Front

If the opposite side is 8 and the adjacent side is 6, what is the tangent of the angle?

Back

tan(θ) = opposite/adjacent = 8/6 = 1.33.

Front

What is the relationship between sine, cosine, and tangent?

Back

tan(θ) = sin(θ)/cos(θ).

Front

What is the formula to find the length of a side using sine?

Back

To find the length of the opposite side: opposite = hypotenuse × sin(θ).