Çözüldü Law of Sines - Trigonometry - Rationalizing The Denominator of Radical Numbers

From an ACT practice test;

If, at a certain moment, a flying kite string forms an angle of elevation of 75° from point A on the horizontal ground and the angle of elevation of the kite at point B on the same ground, 240 ft from A on level ground, is 45°, then what is the length, in feet, of the string?

A) 60·√3
B) 80·√6
C) 144
D) 180
E) 240

Note: The figure given in the original problem was removed, and the wording was revised accordingly because it was far too easy to solve with the picture. The students must understand only by reading and imagining the triangle.

https://www.act.org/content/dam/act/unsecured/documents/Preparing-for-the-ACT.pdf
[ Page 31, Question 59, Answers: Page 65 (Test 2) ]

Applying the Law of Sines, 240 / sin(180° - 75° - 45°) = String / sin(45°)
String = 240·[ (1 / √2) / (√3 / 2) ]
String = 240·(2 / √6)
String = 240·2·√6 / 6
String = 40·2·√6
String = 80·√6 feet.