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 the Pythagorean theorem.
$a^2+b^2=c^2$a2+b2=c2,
Where:
- $c$c is the length of the hypotenuse, and
- $a$a and $b$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: $c=\sqrt{a^2+b^2}$c=√a2+b2
To find a shorter side: $a=\sqrt{c^2-b^2}$a=√c2−b2
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
Let's look at some examples so we can see this in action.
Practice questions
Question 1
The screen on a handheld device has dimensions $9$9 cm by $6$6 cm, and a diagonal of length $x$x cm.
What is the value of $x$x?
Round your answer to two decimal places.
Question 2
The top of a flag pole is $4$4 metres above the ground and the shadow cast by the flag pole is $9$9 metres long.
The distance from the top of the flag pole to the end of its shadow is $d$d m. Find $d$d, rounded to two decimal places.
Question 3
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 below.
Find the value of $x$x.
Find the value of $y$y.
Round your answer to two decimal places.