Posted by **christina** on Sunday, October 20, 2013 at 10:53pm.

Two sides of a triangle have lengths 15 m and 18 m. The angle between them is decreasing at a rate of 0.08 rad/s. Find the rate at which the area of the triangle is changing when the angle between the sides of fixed length is 120°.

- math -
**Reiny**, Sunday, October 20, 2013 at 11:13pm
Using the formula:

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

A = (1/2)(15(18)sinŲ

A = 135 sinŲ

dA/dt = 135 cosŲ dŲ/dt

given: dŲ/dt = -.08 , and cos 120° = -.5

dA /dt = 135(-.5)(-.08) = 5.4 m^2

when the angle is 120°, the area is increasing at 5.4 m^2/s

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