Basic Trigonometric Ratios
We can identify the sides of a right triangle by describing their location in relation to a given angle.
- The "hypotenuse" is the longest side of a right triangle. It is opposite the right angle.
- The "opposite" is the side that the angle does not touch.
- The "adjacent" is the side that the angle does touch, that is not the hypotenuse.
There are three basic trigonometric ratios:
- The sine ratio: [tex]\sin\theta=\dfrac{opposite}{hypotenuse}[/tex]
- The cosine ratio: [tex]\cos\theta=\dfrac{adjacent}{hypotenuse}[/tex]
- The tangent ratio: [tex]\tan\theta=\dfrac{opposite}{adjacent}[/tex]
We use theta (θ) to represent an angle.
Solving the Question
We are asked to find [tex]\cos(\beta)[/tex] in the triangle.
[tex]\cos\theta=\dfrac{adjacent}{hypotenuse}[/tex]
The side adjacent to β measures 8 units.
The hypotenuse of the right triangle measures 17 units.
[tex]\cos\beta=\dfrac{8}{17}[/tex]
Answer
Therefore, [tex]\cos\beta=\dfrac{8}{17}[/tex].
