Check for Understanding: Solving Right Triangles Using Trig

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 of a right triangle are called the hypotenuse (the longest side opposite the right angle), and the two legs (the sides that form the right 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 (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 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: 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: 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: tan(θ) = opposite/adjacent.

Front

How do you find an angle in a right triangle using trigonometric ratios?

Back

To find an angle, you can use the inverse trigonometric functions: θ = sin⁻¹(opposite/hypotenuse), θ = cos⁻¹(adjacent/hypotenuse), or θ = tan⁻¹(opposite/adjacent).

Front

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

Back

In a right triangle, the angles are related to the lengths of the sides through trigonometric ratios, and the sum of the angles in any triangle is always 180 degrees.

Front

What is the purpose of rounding in trigonometric calculations?

Back

Rounding is used to simplify the results of calculations to a specified degree of accuracy, often to the nearest tenth or degree.

Front

How do you determine the length of a missing side in a right triangle?

Back

To determine a missing side, you can use the Pythagorean theorem or trigonometric ratios, depending on the information given.