Geometry Chapter 8

What is the equation for finding the geometric mean?

Place the two numbers in the extremes section and a variable in the mean space, then cross-multiply and solve.

Where does Mario start in the biggest triangle?

Mario always starts at the right angle of the biggest triangle.

What does Mario's chosen route signify?

Whichever route Mario picks will determine where the side lengths go.

What does a² + b² = c² represent?

It represents a right triangle.

What does a² + b² < c² represent?

It represents an obtuse triangle.

What does a² + b² > c² represent?

It represents an acute triangle.

What is a Pythagorean triple?

Three whole numbers that form a right triangle.

What is one example of a Pythagorean triple?

3-4-5.

What are the sides of a 45-45-90 triangle?

x, x, x√2.

What are the sides of a 30-60-90 triangle?

x, 2x, x√3.

When do you use Pythagorean triples?

When you have at least 2 sides and a GCF.

When do you use the regular Pythagorean theorem?

When nothing else works.

When do you use the 45-45-90 triangle?

If you have a right angle and congruent legs, or when you have congruent base angles.

When do you use the 30-60-90 triangle?

If one of the legs is half as much as the hypotenuse.

What is trigonometry?

The study of right triangles.

What are the three main functions used in trigonometry?

Sine, cosine, and tangent.

What does Theta represent?

It is our 'you are here' sign.

What is the sine function?

Opposite over hypotenuse.

What is the cosine function?

Adjacent over hypotenuse.

What is the tangent function?

Opposite over adjacent.

What is the mnemonic for remembering trigonometric ratios?

SohCahToa.

What is the difference between normal trigonometry and inverse trigonometry?

In normal trig, you are given an angle and solve for a ratio; in inverse trig, you start with a ratio and solve for an angle.

What is an angle of elevation?

You look forward and then 'look' up.

What is an angle of depression?

You look forward and then 'look' down.

What is the order of finding the Law of Sines?

Draw, Code, Box.

What codes work with the Law of Sines?

AAS and ASA.

What laws are equal?

Sine and cosine, but only if the angles are complementary.

What laws are reciprocals?

Tangent and cotangent, but only if the angles are complementary.