Chapter 8 Notes - Honors Geometry

Pythagorean Triple

Set of 3 nonzero whole numbers a, b, and c that satisfy the Pythagorean Theorem

Converse of the Pythagorean Theorem

If the sum of the squares of the lengths of two sides of a triangle is equal to the square of the length of the third side, then the triangle is a right triangle.

If a right triangle is a 30º-60º-90º triangle, then...

The length of the longer leg can be found by multiplying the length of the shorter leg by √(3). The length of the hypotenuse can be found by multiplying the shorter leg by 2.

If a triangle is a 45º-45º-90º triangle, then...

The length of the hypotenuse can be found by multiplying one of the legs by √(2).

The Law of Sines

sinA/a \= sinB/b \= sinC/c *OR* a/sinA \= b/sinB \= c/sinC

The Law of Cosines

a²\=b²+c²-2bcCosA *OR* b^(2)\=c^(2)+a^(2)-2caCosB *OR* c^(2)\=a^(2)+b^(2)-2abCosC

sin(theta) of an acute angle in aright triangle

Opposite side/Hypotenuse

cos(theta) of an acute angle in a right triangle

Adjacent side/Hypotenuse

tan(theta) of an acute angle in a right triangle

Opposite side/Adjacent side

The Ambiguous Case can work be used if...

You are given SSA of a triangle (not always, SSA can also get you one or no triangles)

angle of elevation

the angle formed by a horizontal line and a line of sight to a point above

angle of depression

the angle formed by a horizontal line and a line of sight to a point below