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The problem is asking to find the length of the two equal sides of an isosceles triangle, given that the base is 34.95 inches and each base angle is 26.81°.

To solve this, the hint suggests dividing the isosceles triangle into two right triangles. Here's how we can solve it step-by-step:

### Step-by-Step Solution:

1. **Dividing the Isosceles Triangle**:
   By dividing the isosceles triangle into two right triangles, each right triangle will have:
   - One leg (half of the base) = \( \frac{34.95}{2} = 17.475 \) inches.
   - The angle adjacent to the leg is \( 26.81^\circ \).

2. **Using Trigonometry**:
   To find the length of the equal sides (hypotenuse of the right triangle), we can use the cosine function:
   
   \[
   \cos(26.81^\circ) = \frac{\text{adjacent leg (half of the base)}}{\text{hypotenuse (equal side)}}
   \]
   
   Let \( L \) represent the length of the equal sides:
   
   \[
   \cos(26.81^\circ) = \frac{17.475}{L}
   \]
   
   Solving for \( L \):
   
   \[
   L = \frac{17.475}{\cos(26.81^\circ)}
   \]

3. **Calculation**:
   Now, let's compute the value of \( L \). I'll perform this calculation now.The length of each of the two equal sides of the isosceles triangle is approximately **19.58 inches** when rounded to the nearest hundredth.

Would you like further details or explanations?

Here are 5 related questions for further practice:
1. How would the solution change if the base angles were increased to 30°?
2. What is the height of the isosceles triangle given the base and base angles?
3. Can you find the area of the isosceles triangle using the dimensions provided?
4. How would you use the sine function to solve this problem instead of the cosine function?
5. What if the base were doubled but the base angles remained the same?

**Tip:** When working with trigonometry in triangles, always check if dividing the problem into right triangles simplifies the calculation.

The length of the base of an isosceles triangle is 34.95 inches. Each base angle is 26.81°. Find the length of each of the two equal sides of the triangle. (Hint: Divide the triangle into two right triangles.)

Learn how to calculate the length of the equal sides of an isosceles triangle with a base of 34.95 inches and base angles of 26.81° using trigonometric functions. This problem involves dividing the triangle into two right triangles and applying the cosine function. Suitable for students in Grades 9-12.

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