1

Using the animation of the 30 -60 right triangle on the previous slide, create 3 different 30-60 right triangles. After you create your first right triangle, take a screenshot and upload it into the show your work area. Then input the side lengths and ratios below.

Hypotenuse =

Long Leg =

Short Leg =

=

Hypotenuse =

Long Leg =

Short Leg =

=

Hypotenuse =

Long Leg =

Short Leg =

1

Looking at your three 30-60 right triangles and your group mates' 30-60 triangles
a) What do you notice (similarities/differences)?
b) What do you wonder? (any connections to what we have doing in class the past few weeks)

1

Before we start making up some rules lets talk about

1.73205........

You should of seen when comparing the length of your long leg to the short leg.

The long leg of of 30-60 right triangle is 1.73205 longer than its short leg.

On your calculator, find the decimal approximation for

So we can also now say that the long leg of of 30-60 right triangle is longer than its short leg.

1

RULES FOR FINDING THE MISSING SIDES OF A 30-60 RIGHT TRIANGLE WHEN GIVEN ONE SIDE

Using the ratios that you found in Slide 1, lets develop some rules that we can use to find missing sides of a 30-60 Right Triangle.

To find the HYPOTENUSE when given the SHORT LEG
To find the SHORT LEG when given the HYPOTENUSE

To find the LONG LEG when given the SHORT LEG

To find the SHORT LEG when given the LONG LEG

1

BIG PAWS ---> Let's summarize our 30 - 60 Right Triangle Rules / Ratios

30 - 60 Right Triangle Practice Problems

Given Short Leg

1

If

, find:

*Keep answers in simplified radical form

1

If

, find:

*Keep answers in simplified radical form

1

*Keep answers in simplified radical form

1

*Keep answers in simplified radical form

1

*Keep answers in simplified radical form

1

*Keep answers in simplified radical form

1

*Keep answers in simplified radical form

1

*Keep answers in simplified radical form

30 -60 Right Triangle Practice Problems

Given the HYPOTENUSE --> find the short leg and the long leg

1

*Keep answers in simplified radical form

1

*Keep answers in simplified radical form

1

*Keep answers in simplified radical form

1

*Keep answers in simplified radical form

1

*Keep answers in simplified radical form

1

*Keep answers in simplified radical form

1

*Keep answers in simplified radical form

1

*Keep answers in simplified radical form

1

*Keep answers in simplified radical form

30 60 Right Triangles Practice Problems

Given Length of Long Leg

1

*Keep answers in simplified radical form

1

*Keep answers in simplified radical form

1

*Keep answers in simplified radical form

BIG PAWS --> RATIONALIZE THE DENOMINATOR

Before we work on the next set of problems --> We need to talk about radical expressions that contain a radical in the denominator

For a radical expression to be considered simplified, there must be NO radical in the denominator

If there is a radical in the denominator --> you must RATIONALIZE the denominator

1) Multiply BOTH the numberator and denominator by the radical in the denominator

2) Simplify (in the denominator there should be a rational number -->

See next side for some examples

1

Lets do some RATIONALIZING the DENOMINATOR Problems Together

1

*Keep answers in simplified radical form

1

*Keep answers in simplified radical form

1

*Keep answers in simplified radical form

30 - 60 Right Triangle Problems

Given Long Leg and need to rationalize the Denominator

1

*Keep answers in simplified radical form

1

*Keep answers in simplified radical form

45 - 45 (Isosceles) Right Triangles

1

Using the animation of the 45 -45 right triangle on the previous slide, create 3 different 45 - 45 right triangles. After you create your first right triangle, take a screenshot and upload it into the show your work area. Then input the side lengths and ratios below.

Hypotenuse =

Leg 1 =

Leg 2 =

=

Hypotenuse =

Leg 1 =

Leg 2 =

=

Hypotenuse =

Leg 1 =

Leg 2 =

1

Looking at your three 45 - 45 right triangles and your group mates' 45 - 45 triangles
a) What do you notice (similarities/differences)?
b) What do you wonder? (any connections to what we have doing in class the past few weeks)

1

Before we start making up some rules lets talk about

1.414213........

You should of seen when comparing the length of your hypotenuse to leg.

The hypotenuse of of 45- 45 right triangle is 1.414213 longer than its leg.

On your calculator, find the decimal approximation for

So we can also now say that the hypotenuse of 45-45 right triangle is longer than its leg.

1

RULES FOR FINDING THE MISSING SIDES OF A 45 -45 RIGHT TRIANGLE WHEN GIVEN ONE SIDE

Using the ratios that you found in Slide 1, lets develop some rules that we can use to find missing sides of a 45 - 45 Right Triangle.

To find the HYPOTENUSE when given the LEG
To find the LEG when given the HYPOTENUSE

1

BIG PAWS ---> Let's summarize our 45 -45 Right Triangle Rules / Ratios

45 45 Right Triangle Problems

Given LEG

1

45 -45 Right Triangle Practice Problems

Given Hypotenuse

1

45 -45 Right Triangle Practice Problems

Given Hypotenuse with Rationalizing the Denominator

1

Lesson 3 Special Right Triangles

30 - 60 Right Triangle Practice Problems

Given Short Leg

30 -60 Right Triangle Practice Problems

Given the HYPOTENUSE --> find the short leg and the long leg

30 60 Right Triangles Practice Problems

Given Length of Long Leg

30 - 60 Right Triangle Problems

Given Long Leg and need to rationalize the Denominator

45 - 45 (Isosceles) Right Triangles

45 45 Right Triangle Problems

Given LEG

45 -45 Right Triangle Practice Problems

Given Hypotenuse

45 -45 Right Triangle Practice Problems

Given Hypotenuse with Rationalizing the Denominator

More Problems

Lesson 3 Special Right Triangles

Looking at your three 30-60 right triangles and your group mates' 30-60 triangles a) What do you notice (similarities/differences)? b) What do you wonder? (any connections to what we have doing in class the past few weeks)

BIG PAWS ---> Let's summarize our 30 - 60 Right Triangle Rules / Ratios

30 - 60 Right Triangle Practice Problems

Given Short Leg

30 -60 Right Triangle Practice Problems

Given the HYPOTENUSE --> find the short leg and the long leg

30 60 Right Triangles Practice Problems

Given Length of Long Leg

BIG PAWS --> RATIONALIZE THE DENOMINATOR

Before we work on the next set of problems --> We need to talk about radical expressions that contain a radical in the denominator

For a radical expression to be considered simplified, there must be NO radical in the denominator

If there is a radical in the denominator --> you must RATIONALIZE the denominator

1) Multiply BOTH the numberator and denominator by the radical in the denominator

2) Simplify (in the denominator there should be a rational number -->

Lets do some RATIONALIZING the DENOMINATOR Problems Together

30 - 60 Right Triangle Problems

Given Long Leg and need to rationalize the Denominator

45 - 45 (Isosceles) Right Triangles

Looking at your three 45 - 45 right triangles and your group mates' 45 - 45 triangles a) What do you notice (similarities/differences)? b) What do you wonder? (any connections to what we have doing in class the past few weeks)

BIG PAWS ---> Let's summarize our 45 -45 Right Triangle Rules / Ratios

45 45 Right Triangle Problems

Given LEG

45 -45 Right Triangle Practice Problems

Given Hypotenuse

45 -45 Right Triangle Practice Problems

Given Hypotenuse with Rationalizing the Denominator

More Problems

Looking at your three 30-60 right triangles and your group mates' 30-60 triangles a) What do you notice (similarities/differences)? b) What do you wonder? (any connections to what we have doing in class the past few weeks)

BIG PAWS ---> Let's summarize our 30 - 60 Right Triangle Rules / Ratios

BIG PAWS --> RATIONALIZE THE DENOMINATOR

Before we work on the next set of problems --> We need to talk about radical expressions that contain a radical in the denominator

For a radical expression to be considered simplified, there must be NO radical in the denominator

If there is a radical in the denominator --> you must RATIONALIZE the denominator

1) Multiply BOTH the numberator and denominator by the radical in the denominator

2) Simplify (in the denominator there should be a rational number -->

Lets do some RATIONALIZING the DENOMINATOR Problems Together

Looking at your three 45 - 45 right triangles and your group mates' 45 - 45 triangles a) What do you notice (similarities/differences)? b) What do you wonder? (any connections to what we have doing in class the past few weeks)

BIG PAWS ---> Let's summarize our 45 -45 Right Triangle Rules / Ratios

Looking at your three 30-60 right triangles and your group mates' 30-60 triangles
a) What do you notice (similarities/differences)?
b) What do you wonder? (any connections to what we have doing in class the past few weeks)

Looking at your three 45 - 45 right triangles and your group mates' 45 - 45 triangles
a) What do you notice (similarities/differences)?
b) What do you wonder? (any connections to what we have doing in class the past few weeks)

Looking at your three 30-60 right triangles and your group mates' 30-60 triangles
a) What do you notice (similarities/differences)?
b) What do you wonder? (any connections to what we have doing in class the past few weeks)

Looking at your three 45 - 45 right triangles and your group mates' 45 - 45 triangles
a) What do you notice (similarities/differences)?
b) What do you wonder? (any connections to what we have doing in class the past few weeks)