Solve for Triangle Area and Rate of Change at Time t0 | Geometry Problem

[brad sue]

Hi,
I have a problem and I am stuck to one question:

The area of a triangle is given by the formula: A=1/2*b*c*sin(θ )

At time to, we have bo=10 inches, co=20inches, θo=pi/3

a) Find the area of the triangle at to
I found 50*sqrt(3)

b- find the rate of change of the area with respect to b at to.
I found 5*sqrt(3).

c) Find the rate of change of the area with respect with θ at to.
I found 50.

d) Using the rate found in part c) , calculate (by differentials) the approximate change in area if angle theta is increased by one degree.
I need help for this question. I do not know what to do here.

Thank you for your help

 

[lightgrav]

I'm guessing that b is the hypotenuse and c is the leg
that adjoins the angle theta.

I notice that you have ignored the UNITS of these...
units are our friends, and keep us in the right dimension.

As the angle increases, b increases in length and the sine of theta increases.
Both of these will increase the area of the triangle.
When you find out how MUCH, it will have units: in^2 .