Question 240664
distance from ruler to eye is 3 feet.


that's the horizontal distance.


vertical distance is 4 inches = 1/3 of a foot.


the angle that is made is equal to the angle whose tangent is equal to (1/3)/3.


that angle is .11111111... degrees.


the horizontal distance to the cliff is .5 of a mile.  


a mile is 5280 feet.


half a mile is 2640 feet.


that's the horizontal distance.


the vertical distance is x because we don't know it.


tan(.11111111...) = 2/2640 which means that:


x = 2640 * tan(.11111111) which equals 293.33333333... feet which is the same as 293 and 1/3 feet.


you can also do this another way using similar triangles.


distance from the eye to the rule is 3 feet


vertical distance is 1/3 feet. (4 inches = 1/3 feet)


distance from the eye to the cliff is half a mile which is 2640 feet.


vertical distance is x.


since this forms a similar triangle, then:


(1/3) is to 3 as x is to 2640.


ratio formula looks like:


(1/3)/3 = x/2640


cross multiply to get:


(1/3)*2640 = 3x


divide both sides by 3 to get:


(1/3)*2640/3 = x


simplify to get:


293 and (1/3) = x