We have looked at how to find the hypotenuse and the short side of a right-angled triangle. We will now look at how we can apply this theorem to everyday situations. Let's quickly recap Pythagoras' theorem.
Pythagoras theorem: a^{2}+b^{2}=c^{2}, where c is the length of the hypotenuse, and a and b are the lengths of the two shorter sides.
We can rearrange this equation to find formulas for each side length.
To find the hypotenuse: c=\sqrt{a^2+b^2}. To find a shorter side: a=\sqrt{c^2-b^2}
To apply the Pythagorean theorem to real-life situations, we can follow these four simple steps.
Look for right-angled triangles in the scenario.
Sketch a right-angled triangle showing all given information.
Choose which side, hypotenuse or a shorter side, you are trying to find.
Substitute the known values in to the appropriate formula and solve as you would normally.
The screen on a handheld device has dimensions 9 cm by 6 cm, and a diagonal of length x cm.
Find the value of x, correct to two decimal places.
A sports association wants to redesign the trophy they award to the player of the season. The front view of one particular design is shown in the diagram:
Find the value of x.
Find the value of y, correct to two decimal places.
To apply the Pythagorean theorem to real-life situations, we can follow these four simple steps.
Look for right-angled triangles in the scenario.
Sketch a right-angled triangle showing all given information.
Choose which side, hypotenuse or a shorter side, you are trying to find.
Substitute the known values in to the appropriate formula and solve as you would normally.
Investigate Pythagoras’ Theorem and its application to solving simple problems involving right-angled triangles.