Find the lengths of the hypotenuses of all the right triangles in Fig. 3.14 which is referred to as the square root spiral.
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Question

Find the lengths of the hypotenuses of all the right triangles in Fig. 3.14 which is referred to as the square root spiral.

KnowledgeBoat · Accepted Answer

In the square root spiral, each right triangle is formed by taking the hypotenuse of the previous triangle as one leg and adding a perpendicular of length 1 unit as the other leg. Triangle 1 : Both legs = 1 unit. By the Pythagoras theorem : Triangle 2 : Legs = and 1. Triangle 3 : Legs = and 1. Triangle 4 : Legs = 2 and 1. Triangle 5 : Legs = and 1. Triangle 6 : Legs = and 1. Triangle 7 : Legs = and 1. Triangle 8 : Legs = and 1. Triangle 9 : Legs = 3 and 1. Triangle 10 : Legs = and 1. In general, the nth hypotenuse is . Hence, the lengths of the hypotenuses of the right triangles in the square root spiral are and .

Mathematics

Find the lengths of the hypotenuses of all the right triangles in Fig. 3.14 which is referred to as the square root spiral.

Whole Numbers

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Mathematics

Find the lengths of the hypotenuses of all the right triangles in Fig. 3.14 which is referred to as the square root spiral.

Whole Numbers

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