Trigonometry 1

The Trigonometry 1 exercise appears under the High school geometry Math Mission and the Trigonometry Math Mission. The objective of this exercise is to help users find the sine, cosine or tangent measure of any angle in a triangle knowing all three of its sides. 

Types of Problems

This exercise is similar to the exercise, Trigonometry 0.5, just that some of the sides are square root values.

There are three types of problems that show up in this exercise:

1. Find the value of the sine measure of an angle in a triangle - This problem has students look at a triangle and all of its sides and find the sine measure of any angle using the formula ${\text{sin} = \frac{\text{opposite}}{\text{hypotenuse}}}$ - Dividing the side opposite to an angle by the hypotenuse of the triangle.
2. Find the value of the cosine measure of an angle in a triangle - This problem has students look at a triangle and all of its sides and find the cosine measure of any angle using the formula ${\text{cos} = \frac{\text{adjacent}}{\text{hypotenuse}}}$ - Dividing the side next to or adjacent to an angle by the hypotenuse of the triangle.
3. Find the value of the tangent measure of an angle in a triangle - This problem has students look at a triangle and all of its sides and find the tangent measure of any angle using the formula - ${\text{tan} = \frac{\text{opposite}}{\text{adjacent}}}$ -Dividing the side opposite to an angle by the side adjacent to the angle.

Strategies

1. Students can remember the formulas using Sal's "Soh Cah Toa" method in which:
   1. SOH - Sine is equal to Opposite over Hypotenuse
   2. CAH - Cosine is equal to Adjacent over Hypotenuse
   3. TOA - Tangent is equal to Opposite over Adjacent
2. Knowledge of rationalizing denominators can be useful to solve problems in this exercise. You rationalize denominators to simplify fractions like ${\frac{7}{(\sqrt{10})}}$. To simplify this, you multiply both sides of the fraction by $\sqrt{10}$ which gives you ${\frac{(\sqrt[7]{10)}}{(10)}}$ as $\sqrt{10}$ times $\sqrt{10}$ is 10.

Real-life Applications

1. Trigonometry is used in navigation to find the distance between the shore and a point from the sea.
2. Architects use trigonometry to build towers, etc.
3. Trigonometry is also used in finding the distance between celestial bodies
4. Trigonometry has many applications in astronomy, music, analysis of financial markets, and many more professions.