Grade 10

Name sides and angles in 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.

Question 1

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

A right-angled triangle has a vertices are labeled in a counterclockwise direction: vertex $A$`A` is positioned at the top, vertex $B$`B` at the bottom left, and vertex $C$`C` at the bottom right. There are three angles. At vertex $A$`A`, $\angle BAC$∠`BAC` labeled as $\alpha$`α`. At vertex $B$`B`, $\angle ABC$∠`ABC` is labeled as $\theta$`θ`. At vertex $C$`C` is $\angle ACB$∠`ACB` is the right angle denoted by small square. There are three sides, the hypotenuse is the side $overline(AB)$`overline`(`AB`). Side $overline(BC)$`overline`(`BC`) is opposite to angle $\alpha$`α`. $Sideoverline(BC)$`Sideoverline`(`BC`) is adjacent to angle $\theta$`θ`. Side $overline(AC)$`overline`(`AC`) is opposite to angle $\theta$`θ`. $Sideoverline(AC)$`Sideoverline`(`AC`) is adjacent to angle $\alpha$`α`. Side $overline(AC)$`overline`(`AC`) is not adjacent to angle $theta$`theta`.

$AB$AB
A
$BC$BC
B
$AC$AC
C

Question 2

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

A right-angled triangle with vertices labeled A, B, and C. Angle BAC at vertex A is labeled with the Greek letter alpha. Angle ACB at vertex C is labeled as theta (θ). There is a right angle ABC at vertex B, indicated by a square corner. Side AB is adjacent to angle alpha and side BC is the opposite. Side AB is opposite to angle theta and side BC is the adjacent. Side AC is the hypothenuse.

$AB$AB
A
$BC$BC
B
$AC$AC
C

Question 3

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
A
False
B
True or false: According to the angle A, the distance from the $driver$ to the building would be the opposite side.
True
A
False
B

Outcomes

10D.T2.01

Determine, through investigation , the relationship between the ratio of two sides in a right triangle and the ratio of the two corresponding sides in a similar right triangle, and define the sine, cosine, and tangent ratios