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Missing lengths of a 30°-60°-90° Special Right Triangle given Long Leg length = 3√6

Short Leg length =
Long Leg length/√3

Short Leg length =
3√6/√3

Since 6 is divisible by 3, apply the quotient rule for radicals:
√6/√3
=
√
6/3
= √2
Short leg length = 3√2 = 4.242640687119
Hypotenuse length = 2 * Short Leg length
Hypotenuse length = 2 * 3√2
Hypotenuse length = 6√2 = 8.485281374239

The solution above and other related solutions were provided by the 30°-60°-90° Special Right Triangle Application. 

Find Missing Lengths of a 30-60-90 Special Right Triangle

Related Glossary Terms

Hypotenuse

Product Rule for Radicals

Pythagorean Theorem

Right Triangle

Related Applications

Determine whether a Triangle is a Right Triangle

Find Missing Lengths of a 45°-45°-90° Special Right Triangle

Find the Hypotenuse of a Right Triangle | Given Leg Lengths

Find the Square Root of a Number

Related Solutions

Missing lengths of a 30°-60°-90° Special Right Triangle given Hypotenuse length = 15

Missing lengths of a 30°-60°-90° Special Right Triangle given Long Leg length = 72

Missing lengths of a 30°-60°-90° Special Right Triangle given Hypotenuse length = 16

Missing lengths of a 30°-60°-90° Special Right Triangle given Long Leg length = 6

Missing lengths of a 30°-60°-90° Special Right Triangle given Hypotenuse length = 24

Missing lengths of a 30°-60°-90° Special Right Triangle given Long Leg length = 18

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