|
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)   (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
|
|
|
| |
