Question

One side of a triangle is increasing at a rate of 5 cm/s and a second side is decreasing at a rate of 2 cm/s. If the area of the triangle remains constant, at what rate does the angle between the sides change when the first side is 26 cm long, the second side is 32 cm, and the angle is π/4?

Answer 1

Area= 1/2(xysin(theta) then you use partial derivatives. I got that part but I don't understand how Area=1/2 (xy sin(theta))...

Answer 2

If your triangle isn't right triangle, then that is the formula to find Area!

Answer 3

Okay I figured that but any way you could explain how that might convince me so I understand how it was derived?

Answer 4

Do you have the picture?
(My PC likes can't run at this peak time!)

Answer 5

Your PC can't what? I actually don't have a picture for this problem. That's why I was confused.

Answer 6

I suppose (a side)(sin(theta))= height . Then height(another side) (1/2)= area.. Right?

Answer 7

Does this work for right triangles as well?

Answer 8

Yes, it does!
since right triangle already has 2 sides perpendicular, so 1 leg is h!

Answer 9

This formula is applied when we have 2 sides and 1 angle!

Answer 10

Oh right because sin(90)=1 haha. nice

Answer 11

S = (1/2) b * h
h = a Sin C
=> S = (1/2) b * a sin C

Answer 12

Do you see how it related?

Answer 13

Yes, thanks for the help Chlorophyll!

Answer 14

I'm happy when I solve what bothers the askers :)

Answer 15

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