## How to find unknown sides of a triangle using the Rule of Pythagoras.

Goal:

## Theory:

Part 1

This topic shows you the steps for finding unknown sides of right-angled triangles using the rule of Pythagoras.

The rule of Pythagoras states that in any right-angled triangle with legs ‘a’ and ‘b’ and hypotenuse ‘c’,

This rule can be used (a) to f**ind the hypotenuse**, given the two-leg lengths, or (b) to find an unknown leg length, given one of the legs and the hypotenuse.

This is how these problems can be solved…

**(a) find the hypotenuse, ‘c’, given legs ‘a’ and ‘b’ of a right triangle:**

Given: c2 = a2 + b2,

For example, if ‘a’ = 3 and ‘b’ = 4,

then *c*^{2} = 3^{2} + 4^{2}

= 9 + 16

= 25

= 5 (Rejecting negative value of ‘c’.)

**(b) find leg, ‘b’, given leg ‘a’ and hypotenuse ‘c’ of a right triangle.**

Given: *c*^{2} = *a*^{2} + *b*^{2},

so: *b*^{2} = *c*^{2} – *a*^{2}

For example, if ‘a’ = 6 and ‘c’ = 10,

then *b*^{2} = 10^{2} – 6^{2 }

= 100 – 36

= 64

= 8 (Rejecting negative value of ‘b’.)

## Method:

Part 2

Maths Helper Plus shows you to how to solve your own right triangles for unknown sides by using the rule of Pythagoras. The steps below will show you how.

We have created a Maths Helper Plus document containing the completed example from this topic. You can use this to practice the steps described below, and as a starting point for solving your own problems.Step 1Download the free support file…

File name:‘Pythagoras2.mhp’ File size: 17kbClick hereto download the file.If you choose` ‘Open this file from its current location’, then Maths Helper Plus

shouldopen the document immediately. If not, try the other option: ‘Save this file to disk’, then run Maths Helper Plus and choose the ‘Open’ command from the ‘File’ menu. Locate the saved file and open it.If you do not yet have Maths Helper Plus installed on your computer,click herefor instructions.

##### Step 2 Display the parameters box

Press the F5 key to display the parameters box:

You enter the given information into these edit boxes as follows:

edit box ‘**A**‘ = horizontal leg of the right triangle

edit box ‘**B**‘ = vertical leg of the right triangle

edit box ‘**C**‘ = hypotenuse of the right triangle

Set any two of A, B, and C to the values you are given.

Set the unknown value to zero.

Out of the three edit boxes A, B, and C, two will not be zero, and one will be zero.

**NOTE:** In the diagram of the parameters box above, A=3, B=4, and C=0. This means we are solving the problem type where the two legs of the right triangle are given, and we are calculating the length of the hypotenuse.

##### Step 3 Adjust the size of the diagram

If the triangle diagram is too big to display properly on your computer screen, briefly press the F10 key to reduce its size. To make the diagram bigger, hold down a Ctrl key while you press F10.

Download Free Support File

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