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To find the volume of the shape in cubic yards, we need to first determine the volume in cubic feet and then convert it to cubic yards. The shape appears to be a triangular prism.

### Steps to Solve:

1. **Identify the dimensions**:
   - The base of the triangle \( b = 85 \) ft.
   - The height of the triangle \( h \) is unknown.
   - The length of the prism \( l = 56 \) ft.
   - The angle \( \theta = 26^\circ \) is given.

2. **Find the height of the triangle**:
   The height \( h \) of the triangle can be found using the sine function:
   \[
   h = b \cdot \sin(\theta) = 85 \cdot \sin(26^\circ)
   \]

3. **Calculate the area of the triangle**:
   The area \( A \) of the triangle is:
   \[
   A = \frac{1}{2} \cdot b \cdot h
   \]

4. **Find the volume of the prism**:
   The volume \( V \) is the area of the triangle times the length of the prism:
   \[
   V = A \cdot l
   \]

5. **Convert the volume to cubic yards**:
   Since 1 yard = 3 feet, 1 cubic yard = \( 3^3 = 27 \) cubic feet. So, the volume in cubic yards is:
   \[
   V_{\text{yards}} = \frac{V}{27}
   \]

Now, let's perform the calculations.

What is the volume of this shape in cubic yards? θ = 26°, base = 85 ft, length = 56 ft.

Learn how to calculate the volume of a triangular prism with a base of 85 feet, length of 56 feet, and an angle θ = 26°. This guide covers key geometry and trigonometry concepts and provides a detailed step-by-step solution. Suitable for students in Grades 10-12.

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