Answered

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3. two sides of a triangle have lengths 12m and 15m. the angle between them is increasing at a rate of 0.35 radians/minute. a. how fast is the area of the triangle increasing when the angle between the given sides is /6

Sagot :

The area of the triangle will increase at a rate of 3.81 m² per second

Given,

The length of the sides of the triangle are base, 12 m and hypotenuse 15 m

Area of the triangle = 1/2 bh

We have to find h;

That is,

Sin ∅ = opposite side /hypotenuse = h/15

h = 15Sin ∅

d∅/dt = 0.06rad/s

Now,

A = bh/2 = 12 × 15sin∅/2

A = 90sin∅,

By differentiating this equation with respect to A, we have

d(A)/dt = 90cos∅d∅/dt

d(A)/dt = 90cos∅(0.06)

∅ = π/4, cosπ/4 = 0.7071

90×0.7071×0.06

= 3.81m²/s

That is,

The area of the triangle will increase at a rate of 3.81 m² per second

Learn more about rate of increase in area here;

https://brainly.com/question/15098383

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