Pythagorean Theorem: Finding the Missing Leg

Pythagorean Theorem: Finding the Missing Leg

Open Ended

Explain what you think the difference is between when you are finding the missing value of a hypotenuse verses a leg of a right triangle? (compare yesterday's lesson with last night's EdPuzzle)

Find the measure of the hypotenuse: (round to the nearest tenth)

• a² + b² = c²

• 5² + 10² = x²

• 25 + 100 = x²

• 125 = x²

• √125 = √x²

• 11.2 = x

Find the measure of the leg:

(round to the nearest tenth)

• a² + b² = c²

• 8² + x² = 20²

• 64 + x² = 400

• x² = 336

• √x² = √336

• x = 18.3

Now lets try some examples together:

Be sure to follow along and write this down!

Multiple Choice

What is the hypotenuse in this diagram?

• x

• 3

• 11

Multiple Choice

Since 11 is the hypotenuse, what letter are you going to replace with 11 in the pythagorean theorem of a² + b² = c²?

• a

• b

• c

Multiple Choice

That must mean that 3 is one of the legs. What value in the pythagorean theorem will we need to replace with 3?

• a

• b

• It doesn't matter, either will work out just fine :)

Multiple Select

Which TWO equations could you use to solve for x in this diagram?

• 3² + x² = 11²

• x² + 3² = 11²

• 3² + 11² = x²

• 11² + 3² = x²

Multiple Choice

What is the hypotenuse in this diagram?

• 30

• 24

• x

Multiple Choice

Since 30 is the hypotenuse, what letter are you going to replace with 30 in the pythagorean theorem of a² + b² = c²?

• b

• c

• a

Multiple Select

Which TWO equations could you use to solve for x in this diagram?

• 30² + x² = 24²

• x² + 24² = 30²

• 24² + x² = 30²

• 24² + 30² = x²

Wait, did you get the question marked wrong, but you got the right answer?

Chances are that you responded with 18, not 18.0\0! Yes, it does make a difference because the question said to round to the nearest tenth which means the tenth place needs to be shown in your answer! Be careful with rounding and instrucitons!

Multiple Select

Which TWO equations could you use to solve for x in this diagram?

• x² + 12² = 20²

• x² + 20² = 12²

• 12² + 20² = x²

• 12² + x² = 20²

Now it's time for word problems!

Get ready to draw!

A 20-foot ladder is leaned up against a wall. The base of the ladder is 8 feet from the wall, how high up will the ladder reach?

Take a moment and draw a diagram of what you think this situation would look like on your paper before moving on.

Hopefully your diagram will look something like this:

Now please work on the last 4 problems of today's worksheet.

Good Luck!

If the full length of the base of the candy corn is 12 millimeters, and the length of the edge of the candy corn is 20 millimeters, approximately how tall is the candy corn?

Take a moment and draw a diagram of what you think this situation would look like on your paper before moving on.

Hopefully your diagram will look something like this:

This was a very tricky diagram!

If you got this problem wrong:

Chances are you didn't divide the base by 2 to get the leg of one of the triangles to be 6!