Question

Steps For Solving For Missing Sides

1. Decide which Non-Right angle you are going to use

2. Label the given sides based on their relationship to the angle

3. Pick which trig function you are going to use

4. Set up your equation

****Angle measurement ALWAYS goes next to trig function***

5. Solve for x







Solve the following problem. Round to one decimal place if necessary:





Show all your work including your original equation. An example of how your work should look

example = tan(56)= x12


12*tan(56)=x

x=17.79

(3 points)

Answer 1

Of course! To solve for missing sides using the provided steps, let's illustrate the process with a hypothetical problem. For the purpose of this illustration, let's say we have a triangle where angle \( \theta \) is 30 degrees, and the length of the side opposite to the angle \( \theta \) is 5 units. We need to find the length of the adjacent side, represented as \( x \).

Step 1: Decide which non-right angle you are going to use.
- We will use angle \( \theta = 30^\circ \).

Step 2: Label the given sides based on their relationship to the angle.
- Opposite side (to angle \( \theta \)): 5 (let's denote it as O)
- Adjacent side (to angle \( \theta \)): \( x \) (the side we need to find)

Step 3: Pick which trig function you are going to use.
- Since we have the opposite side and need to find the adjacent side, we will use the tangent function:
\[
\tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{O}{x}
\]

Step 4: Set up your equation.
- Our equation using 30 degrees will be:
\[
\tan(30) = \frac{5}{x}
\]

Step 5: Solve for \( x \).
- Cross-multiply to set up the equation:
\[
x \cdot \tan(30) = 5
\]

- Now, we will isolate \( x \) by dividing both sides by \( \tan(30) \):
\[
x = \frac{5}{\tan(30)}
\]

- Next, calculate \( \tan(30) \). The value of \( \tan(30^\circ) = \frac{1}{\sqrt{3}} \approx 0.5774 \).
Therefore, substituting back in:

\[
x = \frac{5}{0.5774} \approx 8.66
\]

Rounding to one decimal place, we have:
\[
x \approx 8.7
\]

So, to summarize the solution:
1. Using \( \theta = 30^\circ \) with opposite side = 5 and adjacent side = \( x \).
2. Set up the equation:
\[
\tan(30) = \frac{5}{x}
\]
3. Solve the equation:
\[
x = \frac{5}{\tan(30)} \approx 8.7
\]

**Final Answer:**
\( x \approx 8.7 \) (the length of the adjacent side)