Sides of a Right-Angled Triangle
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 vertices 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. At vertex $A$A, $\angle BAC$∠BAC is labeled as $\alpha$α. At vertex $B$B, $\angle ABC$∠ABC is labeled as $\theta$θ. At vertex $C$C , $\angle ACB$∠ACB is the right angle denoted by a small square. 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?
$AB$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
AFalse
BTrue or false: According to the angle A, the distance from the driver to the building would be the opposite side.
True
AFalse
B