Explain how the three trig functions can be found by creating a ratio of the side lengths in a right triangle? what are the three trig functions? how can they be written as a ratio of the sides?

Three trigonometric functions are sinФ, cosФ, tanФ

For the shown right triangle ABC, AB is side opposite to angle Ф, BC is side adjacent to angle Ф and side AC is hypotenuse side( side opposite right angle)

All three trigonometioc ratios can be found from sides of triangle by

formulas as written

SinФ =

cosФ =

tanФ =

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).