NZ Level 6 (NZC) Level 1 (NCEA)

Sides of a Right-Angled Triangle

Lesson

We have already seen which of the sides in a right-angled triangle is the hypotenuse.

If we have another angle indicated (like $\theta$`θ` in the diagram below) then we can also label the other two sides with two special names.

**Opposite Side** - is the name given to the side opposite the angle in question

**Adjacent Side** - is the name given to the side adjacent (next to) the angle in question.

Have a look at these triangles that I have named below. Note how the sides adjacent, opposite and hypotenuse are also abbreviated to A, O and H.

Let's have a look at these worked examples.

Which of the following is the opposite side to angle $\theta$`θ`?

$AB$

`A``B`A$BC$

`B``C`B$AC$

`A``C`C$AB$

`A``B`A$BC$

`B``C`B$AC$

`A``C`C

Which of the following is the adjacent side to angle $\theta$`θ`?

$AB$

`A``B`A$BC$

`B``C`B$AC$

`A``C`C$AB$

`A``B`A$BC$

`B``C`B$AC$

`A``C`C

A driver glances up at the top of a building.

True or false: According to the angle A, the height of the building is the opposite side.

True

AFalse

BTrue

AFalse

BTrue or false: According to the angle A, the distance from the driver to the building would be the opposite side.

True

AFalse

BTrue

AFalse

B

Use trigonometric ratios and Pythagoras’ theorem in two and three dimensions

Apply geometric reasoning in solving problems

Apply right-angled triangles in solving measurement problems