Question

An isosceles triangle has equal sides of length 12 inches. If the angel DELTA between these sides is created from 30 degrees to 33 degrees, use differentials to approximate the change in the area of the triangle.

Answer 1

sorry its 0.5 * 12^2 * sin delta

Answer 2

first draw a triangle with a perpendicular to the base from the point of angle delta

Answer 3

now area =0.5 x base x height
the perpendicular will be bisector of the base so you can find the base and height in terms of sin and cos of angle delta/2 and 12 inch side.

Answer 4

now increase the angle by del and correspondingly change the value of sin and cos in the equations. you can now have the variation of the area with change in angle. which is the differential.

Answer 5

Ok so for B=12sin(delta/2) and h=12cos(delta/2). Would this be correct or wrong?

Answer 6

That sentence was awkwardly worded^ was going to say for b i got, and then changed my mind to b=

Answer 7

Or do i have to take into consideration that b is being bisected? so i would get sin(delta/2)= (b/2)/12? which would give me 24sin(delta/2)??