related rates problem

**hazecraze** · October 30th 2009, 01:28 PM

Two sides of a triangle have lengths 9 m and 10 m. The angle between them is increasing at a rate of 0.06 rad/s. Find the rate at which the area of the triangle is increasing when the angle between the sides of fixed length is 60°.

$A=\frac{1}{2}bh$

$\frac{dA}{dt}=\frac{1}{2}[h\frac{db}{dt} +b \frac{dh}{dt}]$

$\frac{dx}{dt}= .06$

How do I relate relate area to the angle?

**skeeter** · October 30th 2009, 02:01 PM

Originally Posted by hazecraze

Two sides of a triangle have lengths 9 m and 10 m. The angle between them is increasing at a rate of 0.06 rad/s. Find the rate at which the area of the triangle is increasing when the angle between the sides of fixed length is 60°.

$A=\frac{1}{2}bh$

$\frac{dA}{dt}=\frac{1}{2}[h\frac{db}{dt} +b \frac{dh}{dt}]$

$\frac{dx}{dt}= .06$

How do I relate relate area to the angle?

you should have learned this in trig ...

$A = \frac{1}{2}ab\sin{\theta}$

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