Pythagoras' Theorem

Pythagorean Theorem: Word Problems

​Objective

• ​Determine the missing side.

Previous knowledge

• How to determine how to find if the triangle is a right triangle.

• Determine the hypotenuse when it given both legs

• Determine the missing legs when give n a leg and the hypotenuse.

Open Ended

Pythagoras' Theorem can be used for 3 purposes:

State them and the equations you would use.

Multiple Choice

Determine if the following triangle with dimensions of : 15, 20, 25 is a Right Angled Triangle

• Yes it is a R.A.T

• No it is not a R.A.T

Fill in the Blanks

Multiple Choice

Determine if the following triangle with dimensions of : 18, 73, 75 is a Right Angled Triangle

• Yes

• No

Fill in the Blanks

Multiple Choice

Correct rearrangement of Pythagoras' Theorem to find shorter side: a

• $$c^2=a^2+b^2$$

• $$a^2=c^2-b^2$$

• $$a^2=c^2+b^2$$

Multiple Choice

a² + b² = c²

^{b = 35}

^{c = 37}

• a = 12

• a = 11

• a = 18

• a = 14

Word Problems

When solving word problems, it helps to draw a triangle and fill in the missing information.

Multiple Choice

You need a ladder that will reach up a 25 metres tall house when placed 10 metres away from the house. How tall does the ladder need to be?

Which diagram best represents the problem?

Multiple Choice

You need a ladder that will reach up a 25 metres tall house when placed 10 metres away from the house. How tall does the ladder need to be?

• 25 m

• 26 m

• 27 m

• 28 m

Multiple Choice

You need a ladder that will reach up a 25 metres tall house when placed 10 metres away from the house. How tall does the ladder need to be?

Which equation could be used to solve the problem?

• $$25^2+10^2=c^2$$

• $$25^2+b^2=10^2$$

• $$a^2+10^2=25^2$$

• $$10^2+b^2=25^2$$

Multiple Choice

Larry attached a string from the top of the flagpole to the ground.  The flagpole is 26 metres high and the string is 18 metres away from the flagpole.  How long is the string? 

• 352 m

• 31.6 metres

• 44 metres

• 6.6 m

Multiple Choice

Madison is on the top of an 80 metre building. She is creating a zipline course to the ground with 100 metres of cable. How far from the base of the building will she need to anchor the cable to make the zipline cable tight?

• 60 m

• 20 m

• 180 m

Multiple Choice

Two joggers run 8 km north and then 5 km west.  What is the shortest distance back to their starting point to the nearest tenth?

• 13 km

• 9.4 km

• 6.2 km

• 9 km

Fill in the Blanks