Two sides of a triangle have lengths 8 m and 24 m. The angle between them is increasing at a rate of 0.05 rad/s. Find the rate at which the area of the triangle is changing when the angle between the sides of fixed length is 135°. Round your answer to two decimal places.

Question

So it would be
Using the formula:

area = (1/2) ab sinØ , where a and b are the sides and Ø is the contained angle

A = (1/2)(8*24)sinØ
A = 96 sinØ
dA/dt = 96cosØ dØ/dt
given: dØ/dt = .05

dA /dt = 96(cos(135)(.05) = -3.40
I keep getting it wrong?

Answer 1

Who says it is wrong?
I get the same result

Make a sketch with the arms at 135° ........ (90+45)
if you increase the angle , you will see that the area is actually getting smaller, (the lines eventually will become a straight line, at which point the area is zero)

at Ø = 134.99° , A = 67.894097
at Ø = 135.01° , A = 67.87040..
notice that the area has decreased slightly for that small increase in the angle

Answer 2

My online homework says it is wrong. I tried it without the negative sign too

Answer 3

-4.78

Answer 4

dA /dt = 96(cos(135)(.05) = -3.39