As soon as I read this, the words "law of cosines" popped into my head. I don't have a good intuitive feeling for the law of cosines, but I went and looked it up (you probably could have done that), and I found that it's exactly what you need for this problem.
The "law of cosines" relates the lengths of the sides of any triangle to the cosine of one of its angles ... just what we need, since we know all the sides, and we want to find one of the angles.
To find angle-B, the law of cosines says
b² = a² + c² - 2 a c cosine(B)
B = angle-B b = the side opposite angle-B = 1.4 a, c = the other 2 sides = 1 and 1.9
(1.4)² = (1)² + (1.9)² - (2 x 1 x 1.9) cos(B)
1.96 = (1) + (3.61) - (3.8) cos(B)
Add 3.8 cos(B) from each side:
1.96 + 3.8 cos(B) = 4.61
Subtract 1.96 from each side:
3.8 cos(B) = 2.65
Divide each side by 3.8 :
cos(B) = 0.69737 (rounded)
Whipping out the trusty calculator: B = the angle whose cosine is 0.69737
= 45.784° .
Now, for the first time, I'll take a deep breath, then hold it while I look back at the question and see whether this is anywhere near one of the choices ...
By gosh ! Choice 'B' is 45.8° ! yay ! I'll bet that's it !
Set this up as ratio with feet on top and minutes on the bottom: . Cross multiply to get 213x = 112 and solve for x to get x = .52 feet. This means that after she has been descending for 8 minutes she is a half a foot from the top.
. Cross multiply to get 213x = 112 and solve for x to get x = .52 feet. This means that after she has been descending for 8 minutes she is a half a foot from the top.