A triangle had two sides of length a and b with an include angle measuring Pi/3 radians. Given that a increases by 5%, b decreases by 6% and the included angle increases by 2%, estimate the percentage increase of area of the triangle.

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- Jul 31st 2011, 06:06 AMRine198estimating percentage increase
A triangle had two sides of length a and b with an include angle measuring Pi/3 radians. Given that a increases by 5%, b decreases by 6% and the included angle increases by 2%, estimate the percentage increase of area of the triangle.

Thanks! - Jul 31st 2011, 06:16 AMe^(i*pi)Re: estimating percentage increase
The area of a triangle is $\displaystyle A = \dfrac{1}{2}ab \sin(C)$

$\displaystyle A_1 = \dfrac{ab\sqrt{3}}{4} \text{ .... (eq 1)}$

$\displaystyle A_1(1+x) = \dfrac{1}{2}(1.05a)(0.94b)\sin\left(\dfrac{1.02\pi }{3}\right) \text{ .... (eq 2)} $

If we tidy up the constants in equation 2 we get $\displaystyle 0.4935ab\sin\left(\dfrac{1.02\pi}{3}\right) \text{ .... (eq 3)}$

Divide eq3 by eq1 to isolate 1+x and then take 1 to get the answer in decimal form which will need changing to percentage - Jul 31st 2011, 06:27 AMRine198Re: estimating percentage increase
i divided equation 3 by eqn 1 which gave me :

A1(1+x)/A1=0.998717

but i don't get where to go from there? - Jul 31st 2011, 07:06 AMe^(i*pi)Re: estimating percentage increase
You can cancel A1: $\displaystyle 1+x = 0.998717$

- Jul 31st 2011, 07:20 AMRine198Re: estimating percentage increase
but that doesn't correspond to the answer give, which is 0.21%