ACTIVITY 6.11
A GASOLINE PROBLEM
781
You are a geology student collecting rock samples in an area of west Texas. On the
way home, you realize that your Jeep is running low on gas, so you stop at a filling
gas for several days
. However, he is certain
that there is a station on a side road up
station. Unfortunately, the attendant
informs you that his station has been without
ahead that should have gas to sell.
A quick phone call confirms this information, and you begin to ask about the exact
location of the station. The attendant's map of the area indicates that the station is
about 10 miles away at an angle of 35°
with the road you are currently traveling.
G (Gas station)
Desert
10 mi.
見
Side road
(Your location)
35°
Main road
7(Intersection)
Your Jeep is equipped with a GPS, so driving through the desert is not a great prob-
lem, although you would prefer to stay on the road. You estimate
that you have
enough gas for 15 miles. Do you have enough gas
to make it to the other station with-
out going through the desert?
This problem can be solved using the triangle above and some trigonometry to de-
termine the distance from you to the intersection, side
YI, and from the intersection
to the gas station, side
IG.
1. With respect to angle Y, select the correct response in parts a and b.
a. the side YI is known as
i. the side opposite angle Y,
ii. the side adjacent to angle Y, or
iii. the hypotenuse
b. the side YG is known as
i. the side opposite angle Y,
ii. the side adjacent to angle Y, or
iii. the hypotenuse
c. the function that relates YI, YG, and angle Y is the
2. a. Set up an equation indicated by Problem 1c.