Question

A right triangle has side lengths d , e , and f as shown below. Use these lengths to find tanx , cosx , and sinx .

Answer 1

To solve for the trigonometric functions of x, we need to recall the ratios they represent as shown below.

$\sin x = \frac{O}{H}$
$\cos x = \frac{A}{H}$
$\tan x = \frac{O}{A}$

where O stands for opposite, A for adjacent, and H for hypotenuse. So, for example, the sine of x is equal to the side opposite of angle x over the hypotenuse. The same goes for cosine and tangent. Using the diagram attached, we have the expressions of the trigonometric functions as shown below.

$\bold{\sin x = \frac{f}{d}}$
$\bold{\cos x = \frac{e}{d}}$
$\bold{\tan x = \frac{f}{e}}$