SOLUTION: Find the volume of an 8 in. Tall right triangular pyramid with a base hypotenuse of 5 in. And a base leg of 3 inches

Question 603142: Find the volume of an 8 in. Tall right triangular pyramid with a base hypotenuse of 5 in. And a base leg of 3 inches
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
The base is a right triangle with a hypotenuse measuring 5 inches and a leg measuring 3 inches.
According to Pythagoras theorem, the other leg must measure 4 inches, because

The triple 3,4,5 is the best known and most popular of the Pythagorean triples, those sets of 3 positive integers with the square of the largest equal to the sum of the squares of the other two.
So the base of that pyramid is a triangle with two perpendicular sides measuring 3 and 4 inches. Calling one of them the base of the triangle, and the other one the height of the triangle, the area of the triangle, In square inches, is calculated as

The volume of a pyramid is 1/3 times the area of the base, times the height of the pyramid.
For the pyramid in the problem, the volume, in cubic inches, is

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