A right triangle has side lengths a, b, and c as shown below.

Mathematics

1 answer:

Musya8 [376]2 years ago

4 0

Answer:

$\bold{\sin x = \frac{b}{c}}\bold{\\\cos x = \frac{a}{c}}\bold{\\\tan x = \frac{b}{a}}$

Step-by-step explanation:

Given that

A right triangle has side lengths a, b, and c

Because you did not attached photo of the right triangle so I will assume that:

Side a is the adjacent (A)
Side b is the opposite (O)
Side c is the hypotenuse (H)

(Please have a look at the attached photo)

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

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

EX: the sine of x is equal to the side opposite of angle x over the hypotenuse. Hence, we have the expressions of the trigonometric functions as shown below:

$\bold{\sin x = \frac{b}{c}}\bold{\\\cos x = \frac{a}{c}}\bold{\\\tan x = \frac{b}{a}}$

Hope it will find you well

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