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

To solve a problem involving missing sides using trigonometric functions, we can follow the steps outlined. Here’s an example problem that we can solve using these steps.

**Problem:**
In triangle ABC, we know the following:
- Angle A = 30°
- Side a (opposite angle A) = 10
- Side b (adjacent to angle A) = x (the side we want to find)

We'll find the length of side b using the tangent function, as we have the opposite side and we want to find the adjacent side.

**Steps to Solve:**

1. **Decide which non-right angle you are going to use:**
- We are using angle A (30°).

2. **Label the given sides based on their relationship to the angle:**
- Opposite side (a) = 10 (opposite to angle A)
- Adjacent side (b) = x (the side we want to find).

3. **Pick which trig function you are going to use:**
- We will use the tangent function because we have the opposite side and we want the adjacent side.
- Recall: \(\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}\)

4. **Set up your equation:**
- Using the tangent function for angle A:
\[
\tan(30°) = \frac{a}{b} = \frac{10}{x}
\]

5. **Solve for x:**
Rearranging the equation:
\[
x \cdot \tan(30°) = 10
\]
\[
x = \frac{10}{\tan(30°)}
\]

Now calculate \(\tan(30°)\):
\(\tan(30°) = \frac{1}{\sqrt{3}} \approx 0.577\)

So substituting that back in yields:
\[
x = \frac{10}{0.577} \approx 17.32
\]

6. **Final rounding:**
Round to one decimal place:
\[
x \approx 17.3
\]

**Conclusion:**
The missing side \(b\) is approximately **17.3**.

**Written Solution:**
Using the steps we've outlined:

\[
\tan(30°) = \frac{10}{x}
\]

\[
\Rightarrow x \cdot \tan(30°) = 10
\]
\[
\Rightarrow x = \frac{10}{\tan(30°)}
\]

\[
\Rightarrow x \approx 17.3
\]