<s>[INST] Trigonometry find area of triangle Triangle ABC is right angeled with right angle at corner C and angle a at corner A. Calculate triangle area if we know that c=|AB|=10 and tan a = 3/2
I get side |AC| = 2
side |CB| = 3
and side |AB| = 10 but this can not be case because it's not pythagoras definition then 
Greetings from RUssia
Vladimir Vlostok
 [/INST] From the tangent of $a$, you know that $\frac{BC}{AC} = \frac{3}{2}$.
So let $BC = 3x$ and $AC = 2x$
By Pythagoras, $AC^2 + BC^2 = AB^2 \implies 13x^2 = 100 \implies x^2 = \frac{100}{13}$
Area of triangle = $\frac{1}{2} AC \cdot BC = 3x^2 = \frac{300}{13}$
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