Let $x$ be the length of one of the equal sides of an isosceles triangle, and let $θ$ be the angle between them. If $x$ is increasing at the rate (1/12) m/h, and $θ$ is increasing at the rate of $\frac{π}{180}$ radius/h, then find the rate in $m^{3}$ / $h$ at which the area of the triangle is increasing when $x = 12 m a n d t h η = π / 4 .$

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Chloe Discussed

Let

x

be the length of one of the equal sides of an isosceles triangle, and let

θ

be the angle between them. If

x

is increasing at the rate (1/12) m/h, and

θ

is increasing at the rate of

\frac{π}{180}

radius/h, then find the rate in

m^{3}

h

at which the area of the triangle is increasing when

x = 12 m a n d t h η = π / 4 .

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