SOLUTION: AB is a line 652 ft long on one bank of a stream, and C is a point on the opposite bank. A=53 degree 18 min and B=48 degree 36 min. Find the width of the stream from C to AB.

Algebra ->  Trigonometry-basics -> SOLUTION: AB is a line 652 ft long on one bank of a stream, and C is a point on the opposite bank. A=53 degree 18 min and B=48 degree 36 min. Find the width of the stream from C to AB.      Log On


   

Question 162648: AB is a line 652 ft long on one bank of a stream, and C is a point on the opposite bank. A=53 degree 18 min and B=48 degree 36 min. Find the width of the stream from C to AB.
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!

Okay, we'll mark point "D" along line "AB" where it extends to point "C" on the opposite bank. So line highlight%28CD%29 is what we're looking for right?
Given:
AB=652ft
Points "A", "B", & "C" forms a triangle, where:
A=%2853%5Eo%2918min=53.3%5Eo, *note 18%2F60=0.30%5Eo
B=%2848%5Eo%2936min=48.6%5Eo, *note 36%2F60=0.60%5Eo
C=180-A-B=180-%2853.3%5Eo%29-%2848.6%5Eo%29
C=78.10%5Eo
We need to get line "CB", by SINE LAW:
sinA%2FCB=sinC%2FAB
CB=%28sinA%2AAB%29%2FsinC=%28sin53.3%5Eo%29%28652ft%29%2F%28sin78.1%5Eo%29
CB=534.239ft
Now, points "B", "C", & "D" forms a right triangle, and we can solve for line highlight%28CD%29 by trigo functions. But 1st we solve for line DB:
cosB=adj%2Fhyp=DB%2FCB
DB=%28cosB%29%28CB%29=%28cos48.6%5Eo%29%28534.239%29
DB=353.30ft ----> REMEMBER
Now, for CD,
sinB=opp%2Fhyp=CD%2FCB
CD=%28sinB%29%28CB%29=%28sin48.6%5Eo%29%28534.239%29
highlight%28CD=400.71ft%29, ANSWER
To check, we use trigo function TANGENT;
tanB=opp%2Fadj=CD%2FDB
CD=%28tanB%29%28DB%29=%28tan48.6%5Eo%29%28353.30ft%29
CD=400.74, close enough! Bec. we're rounding off
Thank you,
Jojo