Ratios and Proportions – ApplicationsName ______
Sketch a picture for each problem, if appropriate. Solve each problem using proportions. Show all your work, including the work you do on the calculator.
1. Matt is 5 feet 10 inches tall. He casts a shadow that is 6 feet 4 inches. At the same time of the day, the light pole he is standing next to casts a shadow that is 20 feet long. How tall is the light pole?
2. Five-foot-tall Amy casts an 84 in. shadow. Her brother Paul is 5 feet, 9 inches. How long would his shadow be a t the same time of the day?
3. Melissa places a mirror on the ground between herself and a building across the street. If she looks into the mirror at cross hairs that she drew on the mirror, she can see into a window of the building. The mirror’s cross hairs are 1.22 m. from her feet and 7.32 m. from the base of the building. Melissa’s eye is 1.82 m. above the ground. How high is the window off of the ground?
4. Jack is trying to determine the distance across a river.
From Pt. P, he sees a tree directly across the river. He then
finds points A and B so that A, P and B are in a line,
and. P is 6 feet from A and
24 feet from B. How far is it across the river?
5. Find the value of the height, h m, in the following diagram at which the tennis ball must be hit so that it will just pass over the net and land 6 meters away from the base of the net.
6. Two ladders are leaned against a wall such that they make the same angle with the ground. The 10' ladder reaches 8' up the wall. How much further up the wall does the 18' ladder reach?
7. Hank needs to determine the distance AB
across a lake in an east-west direction as shown in the
illustration to the right. He can’t measure this distance
directly over the water. So, instead, he sets up a situation
as shown. He selects the point D from where a straight
line to point B stays on land so he can measure distances.
He drives a marker stick into the ground at another point C
on the line between points D and B. He then moves
eastward from point D to point E, so that the line of sight
from point E to point A includes the marker stick at point C.
Finally, with a long measuring tape, he determines that
8. The Golden Ratio, seen even in early structures like the Parthenon, is often used in architecture to create a pleasing balance for the eye. In a Golden rectangle, the ratio of the length to the width is approximately 1.62:1.
a) Draw a rectangle around the Parthenon, from the left most pillar to the right and from the base of the pillars to the highest point. Dylan measures the length of the building and finds it to be 111.5 feet. How tall is the Parthenon?
b) Cards such as credit cards and driver’s licenses are made to fit the golden ratio. If you have a driver’s license that measures 1.8 inches in height, how long would it be?