Find the exact value of sine, cosine, and tangent of a and t for each triangle.

See below  

Step-by-step explanation:

19)

  13² =  4² + AM²

 169 = 16  + AM ²

AM ² = 153

AM =√153 = √(9× 17) = 3√17

sinA = MT /AT  = 4/13

cosA = AM/AT  = (3√17)/13

tanA = MT/AM  = 4/(3√17)   = (4√17)/51

sinT = AM/AT  = (3√17)/13

cosT = MT/AT  = 4/13

tanT = AM/MT = (3√17)/4

20)

10² =  5² + AJ²

100 = 25  + AJ²

AJ² = 75

AJ = √75 = √(25×3) = 5√3

sinA = JT/AT  = 5/10       = ½

cosA = AJ/AT = (5√3)/10 = (√3)/2

tanA = AJ /AJ = 5/(5√3)  = (√3)/3

sinT = AJ/AT = (5√3)/10 = (√3)/2

cosT = AJ/AT = 5/10       = ½

tanT = AJ/JT  = (5√3)/5   = √3