Geometry Academic

UNIT QUESTION: What patterns can I find in right triangles?Standard: MM2G1, MM2G2

Today’s Question:How do we solve 45°-45°-90° right triangles?Standard: MM2G1.b

You will be able to find the lengths of sides of special right triangles

45-45-90

And

30-60-90

In a 45-45-90 triangle…

We will use a reference triangle to set up a proportion then solve.

45-45-90 Right Triangle

1

1This is our reference triangle for the 45-45-90.

2

45

45

45-45-90 Right Triangle

x

x

2x

45

45

904545 2:1:1

Leg:Leg:Hypotenuse2:: xxx

3

3

x

EX: 1 Solve for x

3 2x

a√2a

a

5

5

x

5 2x

EX: 2 Solve for x

a√2a

a

x

345

EX: 3 Solve for x

x 3 2

2

a√2a

a

Extension Problem

The diagonal of a square is 12 inches. Find the area. Round to the nearest tenth.

Area = 72 in.2

12 in.

Extension Problem 2

Given a circle with a diameter of 12 inches, find the length of the hypotenuse ofa right triangle with the right angle at the center.

12 inches

X

Real Life Problem

30-60-90 Right Triangle

12

30

60

This is our reference triangle for the 30-60-90 triangle.

3

We will use a reference triangle to set up a proportion then solve.

906030 2:3:1

Short Leg:Long Leg:Hypotenuse

xxx 2:3:

60

30

x

y

8

4x 4 3 y

Ex: 1 Solve for x and y.

2aa

a√3

60

30

x

24

Solve for x and yEx: 2

2a

a

a√3y

4x 12 3 y

60

30

x

14

x = 7

Ex: 3 Solve for x and y.

y2a

a

a√3

y = 7√3

60

30

x

x = 5

Ex: 4 Solve for x and y

y

5 3

y = 10

2a

a a√3

a = 4.168 in., so 2a = 9.238 in.

Extension Problem

The altitude of an equilateral triangle is 8 inches. Find the perimeter of the triangle.

2a

a

8

60°

30°

a√3

Perimeter = 27.71 inches

A

A person is standing at point A cheering on his favorite team. Round to nearest tenth.

a) Find the height CD of the bleachers.

b) Find the height of the fan at Point A from the ground.

c) Find the distance AB that the fan is from the field at B.

B

D

C

90 feet.

30°

30°

52.0 feet

39.0 feet

77.9 feet

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