Trigonometric ratios are used to relate the sides of a right triangle to its angles. An acute angle is an angle that measures less than 90 degrees.
In a right triangle, we have three sides - the hypotenuse, the opposite side, and the adjacent side. The hypotenuse is the longest side, and it is opposite to the right angle. The opposite side is the side that is opposite to the angle we are interested in, and the adjacent side is the side that is next to the angle we are interested in.
The three trigonometric ratios for an acute angle are:
- Sine (sin): This is the ratio of the opposite side to the hypotenuse. So, sin(theta) = opposite/hypotenuse.
- Cosine (cos): This is the ratio of the adjacent side to the hypotenuse. So, cos(theta) = adjacent/hypotenuse.
- Tangent (tan): This is the ratio of the opposite side to the adjacent side. So, tan(theta) = opposite/adjacent.
These ratios help us find the length of a side of a right triangle when we know the measure of an acute angle and the length of another side. For example, if we know the length of the adjacent side and the measure of an acute angle, we can use the cosine ratio to find the length of the hypotenuse or the opposite side.
Trigonometric ratios are very useful in many fields of math, science, and engineering.