SOLUTION: By holding a ruler 3 feet in front of her eyes as illustrated in the diagram, Carla sees that the top and bottom points of a vertical cliff face line up with marks separated by 4"

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Question 240664: By holding a ruler 3 feet in front of her eyes as illustrated in the diagram, Carla sees that the top and bottom points of a vertical cliff face line up with marks separated by 4" on the ruler. According to the map, Carla is about a half mile from the cliff. What is the approximate height of the cliff rounded to the nearest foot?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
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