SOLUTION: A cliff is 80 feet above the sea. From the cliff the angle of depression to a boat is 35°. How far is the boat from the base of the cliff? Round your answer to one decimal place.

Algebra.Com
Question 585918: A cliff is 80 feet above the sea. From the cliff the angle of
depression to a boat is 35°. How far is the boat from the base
of the cliff? Round your answer to one decimal place.
I don't get this either. Teachers and tutors have tried to help me but they don't explain it in a way that I can comprehend it.
Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!


The object BELOW is the boat and the object ABOVE is the top of the
cliff.

The angle of DEPRESSION is the horizontal from an object ABOVE looking
DOWNward to an object BELOW.

The angle of ELEVATION is the horizontal from an object BELOW looking 
UPward to an object ABOVE.

They are always the same angle because they are alternate interior angles
formed when a tranversal (the line of sight) cuts two parallel (horizontal) lines.

So they are both 35°.

In the right triangle, the side opposite 35° is 80 and the side adjacent
35° is x which is what we are to find, so the trig ration that involves
what we are given *the opposite) and what we are to find *the adjacent
is tangent which is  

tan(35°) = 

Multiply both sides by x

x·tan(35°) = 80

Divide both sides by tan(35°)

x =  = 114.24 feet

Edwin
RELATED QUESTIONS

The angle of depression of a boat which is directly out to sea as observed from the top... (answered by math_tutor2020)
From the top of a 200-foot cliff, the angle of depression to a boat offshore is 15... (answered by Mathtut)
From the top of a 200-foot cliff, the angle of depression to a boat offshore is 15... (answered by stanbon)
The angle of depression to an offshore boat from the top of a 180-foo cliff is 15... (answered by Alan3354)
A boat is 1000 meters from a cliff. If the angle of depression from the top of the cliff... (answered by mananth)
the angle of depression of a boat,65.7m from the base of a cliff is 28.9 how high is the... (answered by KMST)
A boat is 4500 metres from the base of a cliff. The angle of depression from the top of... (answered by Boreal)
From a boat on a lake, the angle of elevation to the top of a cliff is 21°33. If the base (answered by ewatrrr)