Question 1189731
While standing on a 75m tall bridge, given can see two boats.
 From his position on the bridge, the first boat is located on a bearing of 70 degrees and the second boat is located on a bearing of 300 degrees.
 Gavin estimates that the angles of depression for each of the boats are 38 degrees and 47 degrees respectively.
 How far apart are the boats?
:
find the actual distance from the observer to each boat.
a right angle is formed from the water, 75' below the bridge. to the boat.
the distance to boat will be the hypotenuse (h). 
Find the interior angle from the given depression, 90-47 = 43 degrees
Cos(43) = 75/h
h = 102.55 m to one boat
find the distance to the other boat interior angle = 90-38 = 52 degrees
cos(52) = 75/h
h = 121.82 m to the other boat
:
these form the two sides of a triangle from the observer to each boat, the angle at the observer: 300=70 = 230 degrees (A), distance between the boats is a
Use the law of cosines to find a
{{{a^2 = b^2 + c^2 - (2bc)*Cos(A)}}}
{{{a^2 = 102.55^2 + 121.82^2 -2(102.55*121.82) * Cos(230)}}}
You do this tedious math yourself, I got
a = 203.5 m between the boats