Question 980116
The two separate distanaces from top of the lighthouse to the boats form both transversals of two parallel lines as well as hypotenuses of two right triangles.  The angles of depression are also measures of angles of elevation AT each of the boats.


I will answer the second question.


You have lighthouse height, angle opposite, a right angle at base of lighthouse, and you want to find the unknown legs of the two triangles.  The two unknown legs have endpoints extending from one boat to the other boat.  


You can and SHOULD make the drawing.


One triangle:
b for unknown leg,
{{{tan(5)=25/b}}}
{{{b/25=1/tan(5)}}}
{{{b=25/tan(5)}}}


Other triangle:
x for unknown leg,
{{{tan(7)=25/x}}}
{{{x/25=1/tan(7)}}}
{{{x=25/tan(x)}}}


Distance between the boats,
{{{b+x}}}
{{{highlight(highlight(25/tan(5)+25/tan(7)))}}}