SOLUTION: Larry is going camping and his tent is the shape of a triangular prism with isosceles bases. The floor of the tent is 8 feet by 5 feet and the angled side is 6.5 feet long. Is 6 fe
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Question 1017861: Larry is going camping and his tent is the shape of a triangular prism with isosceles bases. The floor of the tent is 8 feet by 5 feet and the angled side is 6.5 feet long. Is 6 feet an accurate height for this tent? Answer by addingup(3677) (Show Source):
You can put this solution on YOUR website! Larry's tent looks like the picture below. We don't care about the 8 feet side-length, the height of the prism is given by the triangle (see the red area).
If you draw a line down the middle of the triangle you have two identical right triangles each with a side of 6.5 and a base of 5/2= 2.5. In "triangle-speak" we now have a short leg of 2.5 and a hypotenuse of 6.5. We need to find the length of the long leg of the triangle.
Then, per Phythagoras:
sqrt(6.5^2-2.5^2)= long leg, which also happens to be the height we are looking for:
sqrt(42.25-6.25)= 6 this is height of Larry's tent.
