The formula for the volume \( V \) of a pyramid is given by:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
In this case, the base area is 75 square inches and the height is 14 inches. Plugging in these values we get:
\[ V = \frac{1}{3} \times 75 \times 14 \]
Calculating this step by step:
- First, calculate \( 75 \times 14 \):
\[ 75 \times 14 = 1050 \]
- Then, calculate \( \frac{1}{3} \times 1050 \):
\[ \frac{1}{3} \times 1050 = 350 \]
Therefore, the volume of the triangular pyramid is:
\[ \boxed{350} \text{ cubic inches} \]