SOLUTION: 1. Find the volume of a right triangular prism whose height is 100 cm and whose base is a right triangle with a hypotenuse of 30 cm in length and an angle to 60 degrees.

Algebra ->  Surface-area -> SOLUTION: 1. Find the volume of a right triangular prism whose height is 100 cm and whose base is a right triangle with a hypotenuse of 30 cm in length and an angle to 60 degrees.       Log On


   

Question 727386: 1. Find the volume of a right triangular prism whose height is 100 cm and whose base is a right triangle with a hypotenuse of 30 cm in length and an angle to 60 degrees.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The base 30-60-90 triangle is half of an equilateral triangle, so using L for the unknown long leg of this triangle, L%5E2%2B15%5E2=30%5E2. The 15 is half a side of the equilateral triangle giving us the given base triangle.
L=sqrt%2830%5E2-15%5E2%29 comes from the just given equation. Now, area of this base triangle is %281%2F2%2915sqrt%2830%5E2-15%5E2%29. The prism is 100 cm high, so the volume of this prism is then %281%2F2%29%2A100%2A15sqrt%2830%5E2-15%5E2%29 cm^2.

With simplification, volume may be shown as 750sqrt%28675%29=11250sqrt%283%29.