topic badge
CanadaON
Grade 9

5.03 Applications in right triangles

Lesson

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 the side-length relationship for right triangles to everyday situations. Remember:

Side-length relationship for right triangles

$a^2+b^2=c^2$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.

Rearranging side-length relationship for right triangles

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=c2b2

To apply the side-length relationship for right triangles to real life situations, we can follow these four simple steps.

  1. Look for right-angled triangles in the scenario
  2. Sketch a right-angled triangle showing all given information
  3. Choose which side, hypotenuse or a shorter side, you are trying to find
  4. 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 $5$5 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 $6$6 metres above the ground and the shadow cast by the flag pole is $13$13 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.

 

Outcomes

9.E1.5

Solve problems involving the side-length relationship for right triangles in real-life situations, including problems that involve composite shapes.

What is Mathspace

About Mathspace