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°,

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step-by-step explanation:

yx = 36

step-by-step explanation:

cos f = opposite side/ hypotenuse

cos f = yw / yx

we know cos f = 4/9 and yw =16

4/9 = 16/yx

multiply each side by yx

4/9 yx = 16/ yx * yx

4/9 yx = 16

multiply each side by 9/4

9/4 * 4/9 yx = 16 *9/4

yx = 36