# math

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plot of land ABCD such that AB = 85m, BC = 75m, CD = 60m, DA = 50m and angle ACB =90 degrees . Determine the area of the plot in hectares correct to two decimal places

• math -

by Pythagoras, I found AC = 40 (that's the easy part)
So the area of triangle ABC = (1/2)(75)(40) = 1500

In triangle ACD , we need an angle, let's find angle D
40^2 = 50^2 + 60^2 - 2(50)(60)cosD
6000cosD = 2500+3600-1600
cosD = 4500/6000 = .75
angle D = 41.41°

area of triangle ACD = (1/2)(50)(60)sin41.41° = 992.156..

total area = 992.16 + 1500 = 2492.16

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