Geometry Chapter 8 Review Trigonometry

Front

What is a special right triangle?

Back

A special right triangle is a right triangle with specific angle measures that allow for easy calculation of side lengths. The two most common special right triangles are the 45-45-90 triangle and the 30-60-90 triangle.

Front

What are the side length ratios in a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the length of the hypotenuse is √2 times the length of a leg.

Front

What are the side length ratios in a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2, where 1 is the length of the side opposite the 30-degree angle, √3 is the length of the side opposite the 60-degree angle, and 2 is the length of the hypotenuse.

Front

How do you find the height of an object using trigonometry?

Back

To find the height of an object, you can use the tangent function: height = distance from the object * tan(angle of elevation).

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

If one leg of a 30-60-90 triangle is 6, what are the lengths of the other sides?

Back

The length of the side opposite the 30-degree angle is 6, the length of the side opposite the 60-degree angle is 6√3, and the hypotenuse is 12.

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 solve for a missing side in a right triangle using trigonometric ratios?

Back

To solve for a missing side, identify the known angle and the sides involved, then use the appropriate trigonometric ratio (sine, cosine, or tangent) to set up an equation and solve for the unknown.