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 of $$(1/12)m/hr$$ and θ is increasing at the rate of π$$180$$ radians $$/hr$$, then the rate in $$m2/hr$$ at which the area of the triangle is increasing when $$x=12m$$ and θ$$=$$π$$4$$

Question

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 of $$(1/12)m/hr$$ and θ is increasing at the rate of π$$180$$ radians $$/hr$$, then  the rate in $$m2/hr$$ at which the area of the triangle is increasing when $$x=12m$$ and θ$$=$$π$$4$$

Infinity Learn · Accepted Answer

Δ$$ABC=12x2sin$$⁡θdΔ$$dt=122xdxdtsin$$⁡θ$$+x2cos$$⁡θdθ$$dt=xdxdtsin$$⁡θ$$+x22cos$$⁡θdθ$$dt=(12)112$$×$$12+1442$$×$$12$$$$π$$$$180=12+$$π$$52$$

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