Find the hypotenuse of a right-angled triangle if its acute angle is 30 degrees, and the leg adjacent to this angle is 8 √3.
| June 23, 2021 | education
Let the hypotenuse of a right-angled triangle be x.
By definition, the cosine of an acute angle is equal to the ratio of the adjacent leg to the hypotenuse.
We have: cos 30 ° = (8√3) / x.
From here we find x = (8√3): cos 30 °.
Knowing that cos 30 ° = √3 / 2, we calculate:
x = (8√3): (√3 / 2) = 8 * 2 = 16.
Answer: 16.
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