Chapter 8: Right Triangles and Trigonometry

8.1: Geometric Mean

Vocab

The geometric mean is $\sqrt{a+b}$ or $\sqrt[3]{a+b+c}$.

TODO: Part 2 of the lesson

8.2: The Pythagorean Theorem and Its Converse

Vocab

A hypotenuse is the longest side of a right triangle.

Pythagorean theorem states that $a^2+b^2=c^2$ ($\sqrt{a^2+b^2}$ ) where a and b represent the two legs of a right triangle and c represent the hypotenuse of the triangle.

The converse of the pythagorean theorem states that when provided with all the sides of a triangle $a^2+b^2=c^2$, c representing the longest side, is true, then the triangle is right.

Pythagorean Inequality Theorems

Inequality	$a^2+b^2>c^2$	$a^2+b^2=c^2$	$a^2+b^2<c^2$
Type	Acute	Right	Obtuse

TODO: Prove pythagorean theorem.

8.3: Special Right Triangles

8.4: Trigonometry

8.5: Angles of Elevation and Depression

8.6: The Law of Sines

8.7: The Law of Cosines