Solving Problems with Trig Exercise 1

Solution: \(a=10\tan (22^\circ)=4.04\)

Solution Method: For this problem, we will use trig ratios to solve for the missing side length. 

The first step is to determine which trig ratio to use to solve the problem. To choose, we look at what is given in the triangle, and what we want to find. We are given an angle measure of \(22^\circ\) and a side length of 10. Specifically, the side of length 10 is adjacent to the angle of \(22^\circ.\) We want to find the side length of a, the side opposite the \(22^\circ.\) So we need a trig ratio that relates the opposite and adjacent side lengths of an angle: tangent. 

Now that we know to use tangent, we set up the trig ratio using the information in the problem. 
    \begin{align*}
        \tan(\theta) &= \frac{opposite}{adjacent} \\
        \tan(22^\circ) &= \frac{a}{10}
    \end{align*}
Now we have an equation we can solve for \(a.\)
    \begin{align*}
        10\tan(22^\circ)&= a \\
        4.04 &= a
    \end{align*}
Note: When using trigonometric functions in your calculator; if the angle measure is given in degrees, make sure your calculator is in degree mode.