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已知弧高2.3,弧长16.3求弦长是多少?
人气:475 ℃ 时间:2020-03-27 11:37:28
解答
设原心角=2a, 半径R
则:
2a=16.3/R
a=8.15/R
R*cosa+2.3=R
R*cosa=R-2.3 --------------(1)
cosa≈1-(1/2)a^2=1-(33.21/R^2)
代入(1)
R-(33.21/R)=R-2.3
33.21/R=2.3
R=33.21/2.3=14.44
弦长=2*(R^2-(R-2.3)^2)^(1/2)
=2*(2.3*(2R-2.3))^(1/2)
=2*61.134^(1/2)
=2*7.82
=15.64
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