To find the area of a triangle, you can use the following formula:
\[ A = \frac{1}{2} \times \text{base} \times \text{height} \]
For Dan's triangle-shaped poster, the base is 36 inches and the height is 30 inches. Plugging these values into the formula gives:
\[ A = \frac{1}{2} \times 36 \times 30 \]
Now, calculating further:
\[ A = \frac{1}{2} \times 1080 = 540 \]
So, the area of the poster is:
\[ \boxed{540} \text{ square inches} \]