A mountaineer has just reached the peak of Mount Rainier, in Washington state. Looking south, she can see Mount Hood, which she knows to be 109 miles from where she stands, and Mount St. Helens, which is 63 miles away. She can't recall the distance between Mount Hood and Mount St. Helens, but she measures the angle between them, from her vantage point, to be approximately $35^\circ$.
Given the information she has, can the mountaineer calculate the distance between Mount St. Helens and Mount Hood? If not, what additional information does she need?

A. Yes, she has enough information to use the Law of Sines to calculate the distance.

B. No, she needs to know whether the angle at Mount Hood is greater than or less than $\frac{\pi}{4}$.

C. No, she needs to know what all the angles in the triangle add up to.

D. No, she needs to know whether the triangle is acute or obtuse.

E. Yes, she has enough information to use the Law of Cosines to calculate the distance.

F. None of the above

If she has enough information to calculate the distance $d$ between Mount Hood and Mount St. Helens, calculate that distance. If there are two possible distances, calculate both distances and enter your answer as a list, with entries separated by commas. If she does not have enough information to calculate the distance $d$ between Mount Hood and Mount St. Helens, then answer $none$.

Hint: