In a right-angled triangle, an acute angle of 30 ° hypotenuse 12, find the smaller leg?

There is a rule: opposite an angle of 30 degrees, there is a leg equal to half of the hypotenuse.

12: 2 = 6

We find the second leg (according to the Pythagorean theorem):

6² + x² = 12²,

36 + x = 144,

x = 144 – 36,

x = 108

x = √108 = √ 9 * 3 * 4 = 6 √3

We compare the two legs and get the answer:

The smallest leg is 6.



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