Answer:
9. AB = (40/3)√3
10. BC = (20/3)√3
Step-by-step 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
