Complex Pythagoras
You now know how to use Pythagoras' theorem to find any side of a right-angled triangle. Sometimes you have to use it more than once in the same problem.
Question
How would you find S in this diagram, where a right-angled triangle has been split in half?
Answer
You cannot find S until you have found the length of the other side of the whole triangle. We will call it \(x\). Note that \(x\) also forms one side of the smaller right-angled triangle.
Looking at this smaller triangle, you will see that:
\({x^2} = {7^2} - {3^2}\)
So \({x^2} = 49 - 9 = 40\)
(We will not calculate \(x=\sqrt{40}\) as we are going to square it again below)
Looking at the bigger right-angled triangle, you will see that:
\({S^2} = {x^2} + {6^2}\)
which means \({S^2} = 40 + 36\)
\({S^2} = 76\)
\(S = \sqrt {76}\)
\(S = 8.72\,(to\,two\,decimal\,places)\)
Now try the example question below.
Question
How would you find \(c\) in this diagram?
Looking at the first triangle, you will see that:
\({a^2} = {1^2} + {1^2} = 2\)
Looking at the next triangle, you will see that:
\({b^2} = {a^2} + {1^2} = 2 + 1 = 3\)
Looking at the last triangle, you will see that:
\({c^2} = {b^2} + {1^2} = 3 + 1 = 4\)
\(C=\sqrt{4}\)
\(So,\,c = 2\)
More guides on this topic
- Determine the gradient of a straight line
- Circle geometry
- Calculating the volume of a standard solid
- Applying the properties of shapes to determine an angle
- Using similarity
- Working with two-dimensional vectors
- Working with three-dimensional coordinates
- Using vector components
- Calculating the magnitude of a vector
- An Approximate History of Co-ordinates