SOLUTION: Show that the area of an equilateral triangle of side 2x is x^2square3, given that tan 60 degrees=square 3 This question is from the chapter of trigonometry:Tangent ratios. Ple

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Question 208064This question is from textbook Longman mathemathics for IGCSE book1
: Show that the area of an equilateral triangle of side 2x is x^2square3, given that tan 60 degrees=square 3
This question is from the chapter of trigonometry:Tangent ratios.
Please help me to solve this problem. It is really urgent. I would be highly obliged if you solve my question. Solve it as soon as possible. Thankyou very much indeed. This question is from textbook Longman mathemathics for IGCSE book1

Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
Show that the area of an equilateral triangle of side 2x is x^2square3, given that tan 60 degrees=square 3
.
Draw a diagram, it'll help you identify what was given and what you need to do.
.
Remember, area of a triangle is (1/2)bh
where
b is base (given as 2x)
h is height
.
So, we need the height.
Since tan = opposite/adjacent
our setup then:
tan(60) = h/(2x/2) = h/x
sqrt%283%29+=+h%2Fx+
x+sqrt%283%29+=+h+
.
area = %281%2F2%29bh
area = %281%2F2%292x%28x+sqrt%283%29%29
area = x%5E2%2Asqrt%283%29