SOLUTION: The angle of elevation of point C from point B is 29 degrees and 42 minutes. The angle of elevation of point C from another point A, which is 31.2 m directly below B, is 59 degrees

Algebra ->  Trigonometry-basics -> SOLUTION: The angle of elevation of point C from point B is 29 degrees and 42 minutes. The angle of elevation of point C from another point A, which is 31.2 m directly below B, is 59 degrees      Log On


   

Question 1161720: The angle of elevation of point C from point B is 29 degrees and 42 minutes. The angle of elevation of point C from another point A, which is 31.2 m directly below B, is 59 degrees and 23 minutes. How high is C from the horizontal line through A?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
29%5Eo%2242%27%22=%2829%2B42%2F60%29%5Eo=29.7%5Eo and 59%5Eo%2223%27%22=%2859%2B23%2F60%29%5Eo=approximately59.38%5Eo (rounded)

Consider the right triangles ACE and BCD.

CD=h , CE=h%2B31.2m and BC=d , so tan%2859.38%5Eo%29=%28h%2B31.2m%29%2Fd and tan%2829.7%5Eo%29=h%2Fd
so
tan%2859.38%5Eo%29%2Ftan%2829.7%5Eo%29=%28h%2B31.2m%29%2Fh --> 1.6898%2F0.5704=1%2B31.2m%2Fh --> 2.96254=1%2B31.2m%2Fh --> 1.96254=31.2m%2Fh --> h=31.2m%2F1.96254
Rounding, we get h=15.9m and h%2B31.2m=15.9m%2B31.2m=highlight%2847.1m%29