Answer:
[tex]x=4.02[/tex]
Step-by-step explanation:
The given triangle is a right triangle, this is indicated by the box around one of the angles, signifying that the angle is a (90) degree angle. Therefore, to solve this problem one must use trigonometric ratios. These ratios are used to describe the relationship between an angle and the sides in a right triangle.
[tex]sin(\theta)=\frac{opposite}{hypotenuse}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\\\\tan(\theta)=\frac{opposite}{adjacent}\\[/tex]
Bear in mind, the names of the sides of the triangle are relative to the angle that one uses to describe it in the triangle. Therefore the (opposite) and (adjacent) sides will change depending on the angle one chooses to look at it from.
In this case, one is given the length of the side opposite the given angle. One is asked to find the measure of the side adjacent to the angle. Therefore, it would make the most sense to use the tangent (tan) ratio.
[tex]tan(\theta)=\frac{opposite}{adjacent}[/tex]
Substitute,
[tex]tan(20)=\frac{9}{x}[/tex]
Manipulate the equation such that it is solved for (x),
[tex]x=\frac{9}{tan(20)}[/tex]
Solve,
[tex]x=4.02[/tex]
