Related Rates Problem: A plane flying with a constant speed of 26 km/min passes over a ground radar station at an altitude of 6 km and climbs at an angle of 35 degrees. At what rate, in km/min is the distance from the plane to the radar station increasing 3 minutes later?
Hint: The law of cosines for a triangle is
c^2 = a^2 + b^2 - 2ab cos(theta)
where theta is the angle between the sides of length a and b.

Question

anonymous · Answer

do you have a picture?

anonymous · Answer

|dw:1320435703975:dw|

anonymous · Answer

how is that.  the 145 from 180 - 35 degrees

anonymous · Answer

you want 
$$y'$$ and you know 
$$x'=26$$ and the hint is that 
$$y^2=6^2+x^2+2\times 6\times x\cos(145)$$

anonymous · Answer

damn i meant 
$$y^2=6^2+x^2-12x\cos(145)$$ not plus

anonymous · Answer

take the derivative, get 
$$2yy'=2xx'-12\cos(145)x'$$ then plug in the numbers to get y'

anonymous · Answer

put 
$$x'=26$$
$$x=3\times 26=78$$ you still need y which you get from 
$$y^2=6^2+78^2-12\times 78(145)$$

lgg23 · Answer

and $$y^{2} = 6^{2}+78^{2}\times78\cos (145)$$ but thanks this really helped.