A Budget Rental Truck is 12 feet 8 inches tall (from the road to the top of the Van). The cab of the truck is 8 feet long and the van is 24 feet long (see diagram below). If the front of the truck is 8 feet from a stoplight suspended 18 feet above the road, how far behind the truck must the driver of a car be so that he can see the stoplight? Assume that the eye of the driver is 4 feet above the road.
Solution:
The answer is 65 feet!
This problem could be solved with geometry using similar triangles or it could be solved with trigonometry.
In the diagram below, L represents the light (which is 18 feet above the road), T represents the back of the truck (which is 8 + 8 + 24 = 40 feet from the light and 12 feet 8 inches above the road), and E represents the eye of the driver in the car (which is 4 feet above the road and x feet behind the truck). You are solving for x.
The three triangles in the diagram are similar, so you can set up the following proportion:
Using the first two parts of this proportion, you obtain:
4x + 4y = 12.67y
Using the first and last parts of this proportion, you obtain:
18y = 160 + 4x + 4y
Solving simultaneously, you obtain y = 30 feet and x = 65 feet.
Using trig, you could solve for the measure of the acute angle
which is common to all three triangles.
The angle = Arctan (5.33 / 40) = 7.59 degrees.
Then substituting in the equation
tan (7.59) = 8.67 / x,
you again obtain 65 feet for the value of x.
Keith Mealy wrote:
I think you forgot to add a second part to this problem:
If driver A actually stays that far behind the rental truck at a light, how long before driver B (the vehicle immediately behind driver A) honks his horn to move up?
a) (Boston) 0.000007 seconds
b) (New York) will not beep, but stick head out window
and yells (HEY, *#&$HEAD, MOVE THE *#&@ UP!!!! WHADDYA
DOING, YOU #&*()@*)!!!! )
c) (Washington DC) Will just pass on the shoulder.
d) (Los Angeles) Will just pass on one of the other 5
lanes in the same direction.
e) (Chicago) What light?
f) (Philadelphia) Will cross double yellow and cut in
in front of driver A, while giving appropriate gesticulation.
Correctly solved by:
| 1. Keith Mealy | Cincinnati, Ohio |
| 2. Renata Sommerville | Austin, Texas |
| 3. Richard K. Johnson | La Jolla, California |
| 4. Kirstine Wynn | Winchester, Virginia |
| 5. Walt Arrison | Philadelphia, Pennsylvania |
| 6. Diana Xing | Fort Collins, Colorado |
| 7. Nick von Keller | Winchester, Virginia |
| 8. Joe Heintz | Manchester, Tennessee |
| 9. Tony Wu | Fort Collins, Colorado |
| 10. Janine Oliver | Winchester, Virginia |
| 11. Jerry Putt | Loudoun Valley, Virginia |
| 12. Geoff Keith | Santa Monica, California |
| 13. Brendan Jones | Winchester, Virginia |