A ship of height 9 meters is sighted from a lighthouse. From the top of the lighthouse, the angle of depression to the top of the mast and the base of the ship equal 30 degrees and 45 degrees respectively. How far is the ship from the lighthouse?

meters

Step-by-step explanation:

For the two angle of depressions one at the top of mast and other at the base will provide two distinct equation is terms of distance between the ship and lighthouse.

Let the distance between the ship and lighthouse be represented by X

y be the vertical distance above height of ship i.e meters.

Equation 1

or

Second equation

Or

Equating both the equation 1 and 2 we get -

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

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