Final answer:
To calculate the height of a cone, use the formula for the volume and trigonometry to find the height.
Step-by-step explanation:
To calculate the height of a cone, given its volume and the angle between the base and the slant height, you need to use the formula for the volume of a cone and trigonometry.
First, use the formula for the volume of a cone: V = (1/3)πr^2h, where V is the volume, r is the radius of the base, and h is the height.
Next, use trigonometry to find the height. The slant height, the radius of the base, and the angle between the base and the slant height form a right triangle. You can use the sine function to relate the slant height, the radius, and the angle: sin(angle) = radius/slant height. Rearrange this equation to solve for the height: h = slant height * sin(angle).