https://file.aiquickdraw.com/mathbot/file/1726191719717642simrz.jpg

The given image shows a shape with the following key measurements:
- One side of 56 ft
- Another side of 85 ft
- The angle between the sides, \( \theta = 26^\circ \)

We are tasked with finding the volume of this shape in cubic yards. The shape in the image resembles a triangular prism, where the triangular base is defined by the two sides (56 ft and 85 ft) and the included angle \( \theta = 26^\circ \).

### Steps to Find the Volume:

1. **Area of the triangular base**:
   To calculate the area of the triangular base, we can use the formula for the area of a triangle when two sides and the included angle are known:
   \[
   \text{Area of base} = \frac{1}{2} a b \sin(\theta)
   \]
   where:
   - \( a = 56 \, \text{ft} \)
   - \( b = 85 \, \text{ft} \)
   - \( \theta = 26^\circ \)

2. **Volume of the prism**:
   Once the area of the triangular base is known,

What is the volume of this shape in cubic yards with given measurements: one side of 56 feet, another side of 85 feet, and an included angle of 26 degrees?

Learn how to calculate the volume of a triangular prism with sides of 56 ft and 85 ft and an included angle of 26 degrees. The problem involves key geometry and trigonometry concepts, using the sine function to find the area of the triangle base and then calculating the volume. Suitable for students in Grades 9-12.

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