Two sides of a triangle have lengths 13 m and 17 m. The angle between them is increasing at a rate of 5 degrees/ min. How fast is the length of the third side increasing when the angle between the sides of fixed length is 60 degrees/min? Round the result to the nearest thousandth if necessary. (Hint: You will need to use the Law of Cosines: )

Question

a. 1.123 m/min
b. 2.149 m/min
c. 2.107 m/min
d. 1.415 m/min
e. 1.085 m/mi

Answer 1

Recall the law of cosines. If the third side is x, then

x^2 = 13^2 + 17^2 - 2*13*17 cosθ
x^2 = 458-442 cosθ

so,

2x dx/dt = 442 sinθ dθ/dt

So, find x when θ=60°, and then just plug in the given numbers to solve for dx/dt.

Answer 2

A) 1.123m/min