Answer:
Well, for triangle rectangles, we have the relations:
Cos(A) = (adjacent cathetus)/(hypotenuse)
Sin(A) = (opposite cathetus)/(hypotenuse)
Tan(A) = (opposite cathetus)/(adjacent cathetus)
Where the adjacent cathetus is the cathetus that is adjacent to the angle, the opposite cathetus is the one that is opposite to the angle, and the hypotenuse is the side that is opposite to the 90° angle.
Here we want to solve 3 to 9.
3) We want to find values sin(D) and sin(E) in that triangle.
Remember the above relationship for the sin function, here will have:
sin(D) = 12/15 = 0.8
sin(E) = 9/15 = 0.6
4)
Sin(E) = 12/37 = 0.3243
Sin(D) = 35/37 = 0.9459
5)
Sin(E) = 45/53 = 0.8491
Sin(D) = 28/53 = 0.5283
6)
Remember that: Sin(A) = (opposite cathetus)/(hypotenuse)
In the image, 5 is the adjacent cathetus to the angle A, and the opposite cathetus to angle A is the one in front of it, 12, then the equation should be:
Sin(A) = 12/13
Now we should use the cosine relationship:
Cos(A) = (adjacent cathetus)/(hypotenuse)
7)
Cos(X) = 27/45 = 0.6
Cos(Y) = 36/45 = 0.8
8)
Cos(X) = 15/17 = 0.824
Cos(Y) = 8/17 = 0.4706
9)
Cos(X) = 13/26 = 0.5
Cos(Y) = (13*√3)/26 = 0.866
