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!
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!
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