Solving Right Triangles using Trigonometry

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

Front

What are the three sides of a right triangle called?

Back

The three sides are called the hypotenuse (the longest side), the opposite side (opposite the angle of interest), and the adjacent side (next to the angle of interest).

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. It is expressed as a² + b² = c².

Front

What is the sine function in relation to a right triangle?

Back

The sine function is defined as the ratio of the length of the opposite side to the length of the hypotenuse. It is expressed as sin(θ) = opposite/hypotenuse.

Front

What is the cosine function in relation to a right triangle?

Back

The cosine function is defined as the ratio of the length of the adjacent side to the length of the hypotenuse. It is expressed as cos(θ) = adjacent/hypotenuse.

Front

What is the tangent function in relation to a right triangle?

Back

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

Front

How do you find the angle using the sine function?

Back

To find the angle θ using the sine function, use the inverse sine function: θ = sin⁻¹(opposite/hypotenuse).

Front

How do you find the angle using the cosine function?

Back

To find the angle θ using the cosine function, use the inverse cosine function: θ = cos⁻¹(adjacent/hypotenuse).

Front

How do you find the angle using the tangent function?

Back

To find the angle θ using the tangent function, use the inverse tangent function: θ = tan⁻¹(opposite/adjacent).

Front

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

Back

In a right triangle, the sum of the two non-right angles is always 90 degrees.