Question

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

Use the information given in the figure to find the length AC.
If applicable, round your answer to the nearest whole number.
The lengths on the figure are not drawn accurately.
A
41
B
85

Answer 1

76 units

Explanation:

You want the length of AC in the given triangular pyramid.

Pythagorean theorem

The Pythagorean theorem can be used to find the lengths of AD and CD.

AD² + 40² = 41²

AD² = 41² -40² = 81 . . . . . = 9²

and

CD² +40² = 85²

CD² = 85² -40² = 5625 . . . . . = 75²

It can also be used to find AC:

AD² + CD² = AC²

81 + 5625 = AC²

AC = √5706 = 3√634 ≈ 76

The length of side AC is about 76 units.

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Additional comment

The Pythagorean theorem tells you the square of the hypotenuse is the sum of the squares of the legs of a right triangle.

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