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0gNanaa
31.08.2019 •
Mathematics
The diagram below shows equilateral triangle abc sharing a side with square acde. the square has side lengths of 4. what is be? justify your answer.
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Ответ:
The angle EAB is 90+60 = 150.
The law of the cosines helps:
BE^2 = AE^2 + AB^2 - 2*AB*AE*cos(150) = 4^2 + 4^2 - 2*4*4*(-sqrt(3)/2)
BE^2 = 16+16+16*sqrt(3) = 16(2+sqrt(3)),
BE = 4*sqrt( 2 + sqrt(3 ) ) Nice number
BE ~ 7.7274 ... ~ 7.73
In fact, if you take a ruler, one can see that the ratio between AB and BE is ~ 1.95 which s the same number.
BE = 4*sqrt( 2 + sqrt(3 ) ) ~ 7.73
Ответ:
150.94 or 151 ft