A, B & C form the vertices of a triangle.
∠
CAB = 90°,
∠
ABC = 67° and AB = 8.6.
Calculate the length of AC rounded to 3 SF.

Work Shown:

tan(angle) = opposite/adjacent

tan(B) = AC/AB

tan(67) = x/8.6

8.6*tan(67) = x

x = 8.6*tan(67)

x = 20.2603303460843  ... make sure your calculator is in degree mode

x = 20.3  .... rounding to 3 significant figures

see diagram below

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47

c

step-by-step explanation: