貨運百科

標題:

maths mc 99 25

發問:

http://img378.imageshack.us/img378/5838/kimkikxj7.jpg how to do? ans:D

最佳解答:

Draw OC, where O isthe centre of the semi-circle. ∠ACB = 90? (∠ in semi-circle) ∴ ∠ABC = 180? -90? - 25? = 65? (∠ sum of Δ) Since OB = OC = 10 / 2 = 5 cm (radius) ∠OCB = ∠OBC = 65? (base ∠s, isos. Δ) ∠BOC = 180? - 65? - 65? = 50? (∠ sum of Δ) Area of sector OBC, A = π(5)2 (50? /360?) = 125π / 36 cm2 Area of ΔABC, A’ = 1/2 OC X OBsin∠BOC = 1/2 (5)2sin50? cm2 Therefore, area ofthe shaded region = A – A’ = 125π/36 – 25sin50?/2 = 1.33 cm2(cor. to the nearest 0.01 cm2) So, the answer is D.

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