F3 maths problems_9－新聞雲

標題:

F3 maths problems

發問:

1) In the figure, ABCD is a rhombus where diagonals AC and BD intersect at O. Given BC=5cm and ∠BAC=50°. Find, correct to 3significant figures, (a) OB and OC, (b)the area of ABCD. Need step, plz!

最佳解答:

1. In ΔABO : ∠BAO = 50°/2 = 25° sin∠BAO = OB/AB sin25° = OB/(5 cm) OB = 5 sin25° cm OB = 2.11 cm (to 3 sig. fig.) n ΔABO : cos∠BAO = OA/AB cos25° = OA/(5 cm) OA = 5 cos25° cm The diagonals of rhombus bisect each other. OC = OA OC = 5 cos25° cm OC = 4.53 cm (to 3 sig. fig.) (b) BD = 2 OB BD = 2 (5 sin25°) cm BD = 10 sin25° cm AC = 2OA AC = 2 (5 cos 25°) cm AC = 10 cos25° cm Area of rhombus ABCD = (1/2) × AC × BD = (1/2) × (10 cos25°) × (10 sin25°) cm2 = 19.2 cm2 (to 3 sig. fig.)

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