prepcalc homework

Question

To find the distance across a river, a surveyor choose points A and B, which are 195 ft apart on one side of the river. She then chooses a reference point C on the opposite side of the river and finds that  and 

Approximate the distance from point A to point C:

Find the distance across the river:

Answer 1

AC = about 197.8 feet

distance across the river = about 194.2 feet

Use the Law of Sines, the 3rd angle = 180-79-51 = 50 degrees

AC/sin51 = 195/sin50

AC = 195sin51/sin50

let y= distance across the river

and let D = a point directly across the river from C

then

tan79 = y/AD

tan51 = y/DB

ADtan79 = DBtan51

ADtan79 =(195-AD)tan51

AD = 37.75

y =ADtan79 = about 194.2