a = 15
b = 23
Step-by-step explanation:
We would apply the trigonometry SOHCAHTOA
The triangle is right angled:
opposite = side opposite the angle 42° = a
adjacent = 17
hypotenuse = b
To get a, we would use tangent ratio (TOA):
tan 42 = opposite/adjacent
tan 42 = a/17
a = 17 tan 42
a = 17(0.9004)
a = 15.3068
Approximately, to the nearest whole number, a = 15
To get b, we would apply cosine ratio (CAH):
cos 42 = adjacent/hypotenuse
cos 42 = 17/b
b (cos 42) = 17
b = 17/cos 42
b = 17/0.7431
b = 22.877
Approximately to the nearest whole number, b = 23