Question 1093922
you have 4 * sin(a) = 3 * cos(a)


solve for sin(a) to get sin(a) = 3/4 * cos(a).


solve for cos(a) to get cos(a) = 4/3 * sin(a).


solve for tan(a) to get tan(a) = sin(a) / cos(a) = 3/4.


you have a 3,4,5 triangle.


one of your acute angles has 3 as the adjacent side and 4 as the opposite side.


the other of your acute angles has 3 as the opposite side and 4 as the adjacent side.


the angle that has 3 as the opposite side and 4 as the adjacent side is your angle of interest.


we'll call that angle(a).


tan(a) = 3/4.


a = arctan(3/4) = 36.86989765 degrees.


using that value for the angle, we get:


sin(36.86989765) = .6


cos(36.86989765) = .8


tan(36.86989765 = .75


we have:


sin(a) = 3/4 * cos(a) = 3/4 * .8 = .6


cos(a) = 4/3 * sin(a) = 4/3 * .6 = .8


solution checks out.


not sure what you needed, but:


sin(a) = .6


cos(a) = .8


sin(a) = 3/4 * cos(a) = 3/4 .8 = .6


cos(a) = 4/3 * sin(a) = 3/4 * .6 = .8


tan(a) = 3/4


a = 36.86989765


without solving for the angle, you would find the hypotenuse of the right triangle by using pythagorus formula of c^2 = a^2 + b^2 where c is the hypotenuse and a is one leg and b is the other leg.


you would get hypotenuse = 5.


it's a 3,4,5 triangle with the angle you are looking for being opposite the side of length 3 and adjacent to the side of length 4.


tan(a) = opp/adj = 3/4


sin(a) = opp/hyp = 3/5 = .6


cos(a) = adj/hyp = 4/5 = .8