Question

What is the length of the hypotenuse of the triangle ABC

what is the length of the shorter leg of triangle ABC
What is the length of the longer leg of triangle ABC
thank you sm!!!!

Answer 1

9. AB = (40/3)√3

10. BC = (20/3)√3

Explanation:

The ratios of side lengths in the "special" 30-60-90° triangle are ...

1 : √3 : 2

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If D is the point where the altitude meets AB, then we have for the left triangle ...

CD : AD : CA = 1 : √3 : 2 = 10 : 10√3 : 20

and, for the right triangle ...

BD : CD : BC = 1 : √3 : 2 = (10/√3) : 10 : (20/√3)

and for the large triangle ...

BC : CA : AB = 1 : √3 : 2 = (20/√3) : 20 : (40/√3)

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9.

The hypotenuse of ΔABC is AB, shown above to be ...

AB = 40/√3 = (40/3)√3

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10.

The shorter leg of ΔABC is BC, shown above to be ...

BC = 20/√3 = (20/3)√3