Question

A triangular pyramid is formed from three right triangles as shown below.

Use the information given in the figure to find the length FH.
If applicable, round your answer to the nearest whole number.
The lengths on the figure are not drawn accurately.
28
53
117

Answer 1

FH = 108

Explanation:

The given figure requires we use the Pythagorean theorem to write two relations involving right triangle side lengths. The Pythagorean theorem tells us the square of the hypotenuse is the sum of the squares of the other two sides.

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Triangle EGH:

EG² = GH² +HE²

GH² = EG² -HE² = 53² -28² = 2025 . . . . . solve for GH², use given values

Triangle FGH:

FG² = GH² +FH²

FH² = FG² -GH² = 117² -2025 = 11664 . . . . solve for FH², use known values

FH = √11664 = 108 . . . . . take the square root

The length FH is 108.