x and a are each acute angles in standard position. sinx = 3/5 and cosa = 12/13
To find the values of x and a, we can use the relations between sine, cosine, and tangent:
sin(x) = opposite/hypotenuse
cos(a) = adjacent/hypotenuse
From the given values, we have:
sin(x) = 3/5
cos(a) = 12/13
To find the opposite side of x, we can use the Pythagorean theorem:
opposite^2 + adjacent^2 = hypotenuse^2
opposite^2 + (5)^2 = (13)^2
opposite^2 + 25 = 169
opposite^2 = 144
opposite = 12
So, the opposite side of x is 12.
Now, we can use the given values and the Pythagorean theorem to find the adjacent side of a:
adjacent = cos(a) * hypotenuse
adjacent = (12/13) * 13
adjacent = 12
So, the adjacent side of a is 12.
In this case, both x and a have the same opposite side and adjacent side, so they must be the same angle. Therefore, we can conclude that x = a.
Hence, x = a = arccos(12/13) (in radians).