Right Triangles
A right triangle is identified because it has an angle of 90° (marked as a little square).
In a right triangle, there is a larger side called the hypotenuse, and two shorter sides called the legs.
Each one of the acute angles in a right triangle has an adjacent leg and an opposite leg. For example, the angle of 45° given in the figure has 15 as the adjacent leg. The hypotenuse is below it, and we'll call it H.
There is a trigonometric ratio called the cosine that relates the adjacent leg of an angle with the hypotenuse as follows:
[tex]\displaystyle\cos \theta=\frac{\text{adjacent leg}}{\text{hypotenuse}}[/tex]
Applying to the given triangle:
[tex]\cos 45^o=\frac{15}{H}[/tex]
Solving for H:
[tex]H=\frac{15}{\cos45^o}=\frac{15}{\frac{\sqrt[]{2}}{2}}=15\cdot\frac{2}{\sqrt[]{2}}\cdot\frac{\sqrt[]{2}}{\sqrt[]{2}}=15\sqrt[]{2}[/tex]
Hypotenuse length:
[tex]15\sqrt[]{2}[/tex]
