Ratio of Sides in Right-Angled Triangles
Right-angled triangle
In the above right-angled triangle $c$c is the the hypotenuse and $\angle RPQ$∠RPQ is $90^\circ$90°
Now if we call $\angle PQR=\theta$∠PQR=θ and we can identify the opposite and adjacent sides with respect to that angle, (we did this here, if you need to refresh). So $b$b is the opposite side, and $a$a is the adjacent side.
A ratio is a statement of a mathematical relationship between two objects, often represented as a fraction. Various ratios of the following can be constructed from the right-angled triangle with respect to angle $\theta$θ.
$\frac{Opposite}{Adjacent}=\frac{b}{a}$OppositeAdjacent=ba
$\frac{Adjacent}{Hypotenuse}=\frac{a}{c}$AdjacentHypotenuse=ac
$\frac{Opposite}{Hypotenuse}=\frac{b}{c}$OppositeHypotenuse=bc
Examples
Question 1
Considering the angle $\theta$θ, what is the value of the ratio $\frac{Adjacent}{Hypotenuse}$AdjacentHypotenuse ?
Think: First we need to identify which sides are the adjacent and hypotenuse with respect to angle theta. I can see that $BA$BA is the hypotenuse, $AC$AC is the opposite side and $BC$BC is the adjacent.
Do: $\frac{Adjacent}{Hypotenuse}$AdjacentHypotenuse = $\frac{BC}{AB}=\frac{5}{13}$BCAB=513
Question 2
Question 3
Consider the angle $\theta$θ.
What is the value of the ratio $\frac{Opposite}{Adjacent}$OppositeAdjacent?
Express your answer as a fraction.
