Test Review

Math II Day 21 (9-2-10) Standard MM2G1.a Determine the lengths of sides of 30-60-90 triangles. Today’s Question: How do I find the length of a side of a right triangle with only one side and an angle given?

What do you know about Triangles hypotenuse Area = (1/2)bh a2 + b2 = c2 isosceles right equilateral altitude 180 degrees 3 sides short leg long leg

Pythagorean Theorem Review 5 a2 +b2 = c2 c a a2 +42 = 52 ? a2 +16 = 25 4 b a2 = 9 a = 3

Pythagorean Theorem Review 20 a2 +b2 = c2 c a 10 ? b Your final answer should be simplified, not a decimal

Find the measure of the missing side of each triangle. 5.1 Special Right Triangles Groups of 2 5 minutes Learning Task – Part 1 Find the measure of the missing side of each triangle.

30-60-90

Special Right Triangles Short Leg:Long Leg:Hypotenuse

We will use a reference triangle to set up a proportion then solve. 30-60-90 Right Triangle 60 2 1 30 This is our reference triangle for the 30-60-90 triangle. We will use a reference triangle to set up a proportion then solve.

30-60-90 Right Triangle 60 2x x 30

30-60-90 Right Triangle 30 60 90 x x√3 2x SS LS HYP 60 2x x 30

Ex: 1 Solve for x and y. 60 30 60 90 x x√3 2x SS LS 8 8 2x x A 30 B x√3

Solve for x and y B x√3 30 A x 2x 24 60 30 60 90 x x√3 2x SS LS 24 Ex: 2 B x√3 30 30 60 90 x x√3 2x SS LS 24 A x 2x 24 60

y = 7√3 x = 14 30 2x A B x√3 60 x 7 30 60 90 x x√3 2x 7 LS HYP Ex: 3 Solve for x and y. 30 60 90 x x√3 2x 7 LS HYP 30 2x A B x√3 60 x 7 y = 7√3 x = 14

y = 10 x = 5 x A x√3 60 30 B 2x 30 60 90 x x√3 2x SS 5√3 HYP Ex: 4 Solve for x and y x 30 60 90 x x√3 2x SS 5√3 HYP A x√3 60 30 B 2x y = 10 x = 5

2x x√3 x 30 60 90 x x√3 2x SS 8 HYP Extension Problem The altitude of an equilateral triangle is 8 inches. Find the perimeter of the triangle. 30 60 90 x x√3 2x SS 8 HYP 30° 2x x√3 8 60° x

Classwork Pg 153 #7-9

Homework Page 155 #1-9 (odd), 14, 17-21