Trigonometry
Hong Kong
Stage 1 - Stage 3
PYTHAG - Applications using Pythagoras
Lesson
Remember Pythagoras' Theorem?
Pythagoras' 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 other two sides
We can rearrange this equation to find formulas for each side length.
Rearranging Pythagoras' Theorem
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 Pythagoras' Theorem to real life situations,
- Look for right-angled triangles
- Choose which side, hypotenuse or a shorter side, you are trying to find
- Find the lengths of the other two sides
- Apply the relevant formula and substitute the lengths of the other two sides
Let's look at some examples so we can see this in action.
Worked Examples
Question 1
Consider a cone with slant height $13$13m and perpendicular height $12$12m.
Find the length of the radius, $r$r, of the base of this cone.
Hence, find the length of the diameter of the cone's base.
Question 2
Find the length of the unknown side, $x$x, in the given trapezium.
Give your answer correct to two decimal places.
