Posted by **christina** on Sunday, October 20, 2013 at 11:35pm.

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.

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?

- math -
**Reiny**, Sunday, October 20, 2013 at 11:53pm
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

- math -
**christina**, Sunday, October 20, 2013 at 11:57pm
My online homework says it is wrong. I tried it without the negative sign too

- math -
**Anonymous**, Monday, October 21, 2013 at 12:26am
-4.78

- math -
**Kuai**, Monday, October 21, 2013 at 12:30am
dA /dt = 96(cos(135)(.05) = -3.39

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