Answer:
20 cm
Step-by-step explanation:
Given a prism with a right triangle base and a volume of 480 cm³, you want the height of the prism. The base has one side 8 cm, and hypotenuse 10 cm.
Base edge
The missing edge of the right triangle base can be found using the Pythagorean theorem. It tells us the square of the hypotenuse is the sum of the squares of the other two sides:
b² = c² +a²
10² = 8² +a² . . . . . . . use given lengths
a² = 100 -64 = 36 . . . . subtract 8², simplify
a = 6 . . . . . . . . . . . . . length of side BC
Base area
The area of the right triangle base is ...
A = 1/2bh . . . . . . . . b is the triangle base; h is its height
A = 1/2(6 cm)(8 cm) = 24 cm²
Volume
The volume of the prism is ...
V = Bh . . . . . . . . . . . . . . . where B is the base area, and h is the height
480 cm³ = (24 cm²)h . . . use known values
h = 20 cm . . . . . . . divide by the coefficient of h
The height of the prism is 20 cm.
