Question

given the triangle below, evalute the sine, cosine and tangent

Answer 1

Answer:

The sine, cosine and tangent of angle x are;

$\begin{gathered} \sin x=\frac{9}{15} \\ \cos x=\frac{12}{15} \\ \tan x=\frac{9}{12} \end{gathered}$

Explanation:

Given the triangle in the attached image.

we want to evaluate the sine, cosine and tangent of the angle x;

Recall that;

$\begin{gathered} \sin \theta=\frac{opposite}{hypotenuse} \\ \cos \theta=\frac{adjacent}{hypotenuse} \\ \tan \theta=\frac{opposite}{adjacent} \end{gathered}$

From the given figure;

$\begin{gathered} \text{opposite = 9} \\ \text{adjacent = 12} \\ \text{hypotenuse = 15} \end{gathered}$

substituting the given values, we have;

$\begin{gathered} \sin x=\frac{opposite}{hypotenuse}=\frac{9}{15} \\ \cos x=\frac{adjacent}{hypotenuse}=\frac{12}{15} \\ \tan x=\frac{opposite}{adjacent}=\frac{9}{12} \end{gathered}$

Therefore, the sine, cosine and tangent of angle x are;

$\begin{gathered} \sin x=\frac{9}{15} \\ \cos x=\frac{12}{15} \\ \tan x=\frac{9}{12} \end{gathered}$