Question

A right triangle has side lengths d, e, and f as shown below. Use these lengths to find tan x, sin x, and cos x.tan x=sin x=cos x=

Answer 1

From the figure, the following pieces of information are given:

x = angle

d = hypotenuse

f = opposite side

e = adjacent side

Let's recall the formula of the 3 main trigonometric functions and their ratios, then let's plug in the equivalent name of the lengths reflected in the figure:

We get,

$\text{ Tan(x) = }\frac{Opposite\text{ side}}{Adjacent\text{ side}}\text{ = }\frac{f}{e}\text{ }\rightarrow\text{ Tan(x) =}\frac{f}{e}$$\text{ Sin(x) = }\frac{Opposite\text{ Side}}{Hypotenuse}\text{ = }\frac{f}{d}\text{ }\rightarrow\text{ Sin(x) = }\frac{f}{d}$$\text{Cos(x) = }\frac{Adjacent\text{ Side}}{Hypotenuse}\text{ = }\frac{e}{d}\text{ }\rightarrow\text{ Cos(x) = }\frac{e}{d}$