1. estimating 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!

2. Re: estimating percentage increase

The area of a triangle is $A = \dfrac{1}{2}ab \sin(C)$

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

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

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

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

3. Re: 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?

4. Re: estimating percentage increase

You can cancel A1: $1+x = 0.998717$

5. Re: estimating percentage increase

but that doesn't correspond to the answer give, which is 0.21%