Two sides of a triangle have lengths 12 m and 14 m. The angle between them is increasing at a rate of 2°/min. How fast is the length of the third side increasing when the angle between the sides of fixed length is 60°? (Round your answer to three decimal places.) webassig n

1.692 m/min

Step-by-step explanation:

Let be the angle between the two sides and x be the length of the third side. By cosine rule,

We differentiate x with respect to by applying chain rule.

Rate of change of is 2

Rate of change of x is

At 60°,

use an equation of ratios to determine the amount of gas needed to fill the tank.

    0.2             0.8

  =    

288.75             x

                                                              231 gal

so, 0.2x = (0.8)(288.75 gal), and x = = 1155 gal.

                                                                0.2

it would take 1155 gal. to fill the tank.

the cost would be

1155 gal         $3

* = $3465   (answer)

      1           1 gal

hope this you