Just use the cosine law
let x be the distance between them when the angle is Ø
x^2 = 8^2 + 13^2 - 2(8)(13)cosØ
x^2 = 233 - 208cosØ
2x dx/dt = 208sinØ dØ/dt
dx/dt = (104sinØ dØ/dt)/x
given: dØ/dt = .08 rads/min
find : dx/dt when Ø = π/3
we will need x for the case when Ø = π/3.
x^2 = 233 - 208cosπ/3 = 129
x = √129
dx/dt = 104sinπ/3 (.08)/√129
= ....
if get appr. .634 m/min
check my arithmetic
Two sides of a triangle have lengths 8 m and 13 m. The angle between them is increasing at a rate of 0.08 radians /min. How fast is the length of the third side increasing when the angle between the sides of fixed length is π/3 radians.
Please help I have been stuck on this problem for days!
1 answer