Trigonometry 1.5

The  exercise appears under the Trigonometry Math Mission. The objective of this exercise is to help users find the length of sides of triangles knowing all three trigonometric measures of any angle in the triangle.

Types of Problems
There is one type of problem that shows up in this exercise:


 * 1) Use trigonometric measures to solve for missing information of side lengths - This problem has students to look at the trigonometric measures of any angle in a triangle given one side length and solve for any other side length in the triangle. To solve these kind of problems, students can treat the measures like variables.

Strategies
 You can remember the formulas using Sal's soh cah toa method in which:  S O H - Sine is equal to Opposite over Hypotenuse CAH - Cosine is equal to Adjacent over Hypotenuse TOA -  Tangent is equal to Opposite over Adjacent To solve these kind of problems, students can treat the measures like variables. For example, in the picture above we can find out which trigonometric measure is related to ∠ ABC and the sides BC and AB. BC is the side opposite to the angle and AB is the hypotenuse, so we can use the sin function as it deals with the side opposite to an angle and the hypotenuse of an triangle. So we can say that sin(∠ BAC) = 10/x = 5/13. So we get a new equation, 10/x=5/13. We can solve for x to get to know what's the measure of the missing side.</li> </ol>

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