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.
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.
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.