Answer:
To calculate the volume of a triangular pyramid, we can use the formula:
V = (1/3) * B * h
where V is the volume, B is the area of the base, and h is the height of the pyramid.
Since the base of the pyramid is a right-angled triangle, we can use the Pythagorean theorem to find the length of the other two sides, which are the legs of the triangle. The hypotenuse is 6 cm and the angle opposite to the hypotenuse is 30°, so we can use the sine function to find the length of the other leg:
sin(30) = opposite / hypotenuse
opposite = (sin(30) * hypotenuse) = (1/2 * 6) = 3
Now we can use the area formula for a right-angled triangle:
B = (1/2) * base * height = (1/2) * 3 * 6 = 9
To find the height of the pyramid, we can use the fact that all side faces form an angle of 60° with the base. We can use the sine function to find the height of the pyramid:
sin(60) = opposite / hypotenuse
opposite = (sin(60) * hypotenuse) = (√3/2 * 6) = 3√3 cm
Now we can substitute the values of B and h into the volume formula:
V = (1/3) * B * h = (1/3) * 9 * 3√3 = 3√3 cm³
So the exact volume of the triangular pyramid is 3√3 cm³.
Explanation: