Right Triangle Trigonometry

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): a² + b² = c².

Front

What is the sine function in a right triangle?

Back

The sine function (sin) 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 function in a right triangle?

Back

The cosine function (cos) 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 function in a right triangle?

Back

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

Front

What is the inverse sine function?

Back

The inverse sine function (sin⁻¹) is used to find the angle whose sine is a given value.

Front

What is the inverse cosine function?

Back

The inverse cosine function (cos⁻¹) is used to find the angle whose cosine is a given value.

Front

What is the inverse tangent function?

Back

The inverse tangent function (tan⁻¹) is used to find the angle whose tangent is a given value.

Front

How do you find the length of a side using the Pythagorean Theorem?

Back

To find the length of a side, rearrange the Pythagorean Theorem: c = √(a² + b²) for the hypotenuse, or a = √(c² - b²) for one leg.

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2.