We will solve as follows:
First, we are given one angle (35°) and since the problem describes a distance with respect to that angle we will have that the angle belongs to a rigth triangle.
Now, we will find the supplementary angle "s":
[tex]s=90-35\Rightarrow s=55[/tex]Now, we determine the distance with the information given:
[tex]\tan (55)=\frac{x}{199}\Rightarrow x=199\tan (55)[/tex][tex]\Rightarrow x=284.2014533\ldots\Rightarrow x\approx284[/tex]So, the ship is approximately 284 feet from the base of the lighthouse.
Here we can see the angle of depression, so we need to find the angle that is complemetary to it "a", so when they are added equals 90°:
angle of depression + angle "a" = 90°.
Then:
[tex]\tan (a)=\frac{x}{h}[/tex][tex]\Rightarrow x=h\tan (a)[/tex]
