The sides of a 30 60 90 triangle are 9 and 18.What is the third length of the triangle

 15.59 or 9√3

Step-by-step explanation:

We can use the Pythagorean Theorem to calculate the third side.

c² = a² + b²   In a 30 60 90 Triangle, the hypotenuse is twice the length of the short leg of the right angle.

c is the hypotenuse. a is the short leg

18² = 9² + b²

324 = 81 + b²  Subtract 81 from both sides.

324 - 81 = b²  becomes b² = 243   Take the square root of both sides

b = 15.5884 . This can  be rounded to 15.59 or 15.6 depending on significant digits or amount of precision required.

The proportions of the sides of the 30 60 90 triangle can also be used:

2² = 1² + b²

4 = 1 + b²

3 = b²

√3 = b

You can always multiply the length of the short leg by √3 to get the length of the side opposite the 60° angle

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