Answer:
35.4
Step-by-step explanation:
AB is the hypotenuse, and you are looking to find the length of the hypotenuse. Use your known angle, 57 degrees, and your known length, 19.3 cm. We know that cosine is adjacent over hypotenuse, and since 19.3 is the adjacent side and the AB is the hypotenuse, we can use cosine to solve here.
cos 57º=(19.3)/(AB).
With some simple algebra, we can manipulate this equation to look like this:
AB=19.3/(cos 57º).
Plug that into your calculator, and round to the nearest 10th of a cm, and you get 35.4 cm.
If you want to double check your answer (no calculator involved here), you can remember that cos 60º=cos (2π/3)=1/2, so since 60º is pretty close to 57º, you could eyeball it and see that the length is going to be pretty close to 38.6 cm (19/(1/2)). Since your final answer 35.4 cm is relatively close, you can be sure you got the right answer just from your knowledge of the unit circle.
Hope this helps!
