Trig Angles and Sides

Front

What is a trigonometric angle?

Back

A trigonometric angle is the angle formed by the rotation of a ray about a fixed point, typically measured in degrees or radians.

Front

Define sine (sin) in relation to a right triangle.

Back

Sine (sin) is the ratio of the length of the opposite side to the length of the hypotenuse in a right triangle.

Front

Define cosine (cos) in relation to a right triangle.

Back

Cosine (cos) is the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle.

Front

Define tangent (tan) in relation to a right triangle.

Back

Tangent (tan) is the ratio of the length of the opposite side to the length of the adjacent side in a right triangle.

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 measure of an angle using sine?

Back

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

Front

How do you find the measure of an angle using cosine?

Back

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

Front

How do you find the measure of an angle using tangent?

Back

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

Front

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

Back

The sum of the angles in a right triangle is always 180 degrees, with one angle being 90 degrees.

Front

If a hawk swoops down at a 30-degree angle to reach a mouse 15 feet away, how do you calculate the distance from the tree branch to the mouse?

Back

Use the sine function: distance = hypotenuse = opposite/sin(angle). Here, hypotenuse = 15/sin(30°) = 30 feet.