Question

Find the exact value of sine, cosine, and tangent of A and T for each triangle.

Answer 1

See below

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