1. Test Review

2. Math II Day 21 (9-2-10)
Standard MM2G1.a
Determine the lengths of sides of 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?

3. 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

4. Pythagorean Theorem Review5
a2 +b2 = c2 c a
a2 +42 = 52 ?
a2 +16 = 25 4 b
a2 = 9
a = 3

5. Pythagorean Theorem Review20
a2 +b2 = c2 c a 10 ? b
Your final answer should be simplified, not a decimal

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

8. Special Right Triangles
Short Leg:Long Leg:Hypotenuse

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

10. Right Triangle
60 2x x
30

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

12. 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

13. 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

14. 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

15. y = 10 x = 5 x A x√3 60 30 B 2x 30 60 90 x x√3 2x SS 5√3 HYP
Ex: 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

16. 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

17. Classwork
Pg 153 #7-9

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