# Lesson 5: Right Triangle Trigonometry. Trig ratios

Right triangle trigonometry is a branch of mathematics that deals with angles and sides in a right triangle.

A right triangle is a triangle with one right angle. The other two angles add up to 90^{o}. Together, the sum of all interior angles in a right triangle is 180^{o}.

The side relationships in a right triangle are based on the Pythagorean Theorem. If the triangle is right, then the following will be true for the three sides of the triangle:

c^{2} = a^{2} + b^{2} where a and b are shorter sides and c is the longest side.

When the lengths of any two sides are known, the third side can always be found using the Pythagorean Theorem.

When two sides are given and a measure of an angle other than the right angle needs to be found. Or only one side and an angle other than the right angle are given – trigonometric ratios should be used.

Trigonometric ratios are ratios between any two sides of a right triangle that can then be used to determine the measure of an angle between those two sides.

Primary trigonometric ratios (in a right triangle trigonometry) are:

sin(x), cos(x) and tan(x)

sin(x) = opposite/hypotenuse

cos(x) = adjacent/hypotenuse

tan(x) = opposite/adjacent

In this lesson we are discussing how to use these ratios to find angles and side lengths in right triangles.

We are also looking at some special angles and their trigonometric ratios. We are discovering sines and cosines of common angles. These angles are frequently used and their trigonometric ratios should be memorized just like the multiplication tables.

Right triangle trigonometry is widely used on engineering and construction. For example, when homes are designed and built, it is crucial that architects and builders accurately determine and construct the angles of the roof. There are tools for that, however, it is always good to understand the concept and be able to double check.