17. A playgroup school is looking to refurbish the playground area that is in almost a triangular shape (ABC). There is a small tree, almosta vertical line in shape, lets say AD, at the corner
of the playground area
Answers
Given : a triangular shape (ABC).
AD small tree, almost a vertical line in shape,
To Find : Height of Tree AD
Length of Path BC
Area of field ABC
Shortest distance from A to Path BC
Length of BD
Solution:
Height of Tree AD
Tan 30° = AD/AB
AB = 180 m
=> 1/√3 = AD/180
=> AD = 180/√3
=> AD = 60√3 m
BC² = AB² + AC²
=> BC² = 180² + 33²
=> BC² = 32400 + 1089
=> BC² = 33489
=> BC = 183 m
Area of field ABC = (1/2)) * AB * AC
= (1/2) * 180 * 33
= 2,970 m²
Shortest distance from A to BC = AE
(1/2) * BC * AE = (1/2)) * AB * AC
=> 183 * AE = 180 * 33
=> AE = 32.46
=> AE = 32.5 m
Cos 30 = AB/BD
=> √3/2 = 180/BD
=> BD = 360/√3
=> BD = 120√3
=> BD = 207.8
=> BD = 208 m
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