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 9
Homework Statement
The angles in triangle ABC form an increasing arithmetic sequence.
The ratio of angles A:B:C can be written in the form 185:370:555 respectively.
You are told that the total area of the triangle is 9
Length BC is
Given the area of triangle ABC, work out the value of
Give your answer in the form
You must not make any assumptions
You must show all your working
Homework Equations
[/B]
I've attempted to use ##1/2*ab*SinC## presumed it's a right angle.
Area of a triangle: ##1/2*bh##.
Pythagorean Law.
The Attempt at a Solution
I've attempted to firstly figure out the angles of the triangle. I know that they form an increasing arithmetic sequence. So I've used a multiplier of 6/37 which I obtained by:
Let multiplier = ##y##
##y(185+370+555) = 180##
##1110y=180##
##y = 6/37##
On the diagram the angles aren't exactly labelled, so on the bottom left its angle A, bottom right is Angle C and top right is Angle B.
Angle A: ##6/37*185 = 30##
Angle B: ##6/37*370 = 60##
Angle C: ##6/37*555 = 90##
##30, 60, 90## are an increasing sequence by ##+30## each time.
BC = ##x##
Using Trig, ##Sin(30) = Opp/Hyp## Hypotenuse (BA) is ##2x##.
Using Law of Pythagorean = ##a^2+b^2 = c^2##
##(2x)^2  x^2 = AC##
##4x^2  x^2 = AC##
##3x^2= AC##
##AC= \sqrt 3 x##
Not sure how to progress from here. Any guidance? Thank you.
[/B]
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