# Given a right triangle, let x be one of its acute angles. Suppose that the side opposite to angle x has length 15 and that the side adjacent to angle x has length 23. How do you find the approximate value of angle x in radians?

Jun 9, 2016

Start by drawing a diagram.

#### Explanation:

This is right angled trigonometry, so the technique to proceed is via SOHCAHTOA. First, out of $\sin$, $\cos$ and $\tan$ we have to determine which trigonometric function to use.

Here are the definitions:

-$\sin \theta = \text{opposite"/"hypotenuse}$

-$\cos \theta = \text{adjacent"/"hypotenuse}$

-$\tan \theta = \text{opposite"/"adjacent}$

These definitions are extremely important. They will serve you throughout your mathematical career in school. At the beginning, you can remember them with SOHCAHTOA, or Sin = opposite/hypotenuse, etc.

The next step in determining the value of $x$ is seeing what sides we know. It is clearly stated in the problem we know the side opposite $x$ and the side adjacent $x$. Therefore, we use tangent.

Now, we must set up a proportion.

$\tan x = \text{opposite"/"adjacent}$

$\tan x = \frac{15}{23}$

$x = {\tan}^{- 1} \left(\frac{15}{23}\right)$ Note: This can also be noted as $x = \arctan \left(\frac{15}{23}\right)$

$x = 0.58 \text{radians}$

Hopefully this helps!