Mrs. lane’s trigonometry class has been asked to judge the annual unmanned hot-air balloon contest, which has a
prize for highest flying balloon.
a. sarah thinks that the class needs to set up two stations to sight each balloon as it passes between them.
construct a formula that mrs. lane’s class can use to find the height of the balloon by plugging the two angles
of elevation so that they can program their calculators to automatically output the height of the balloon. use
500 ft. for the distance between the stations and and for the angles of elevation.
b. the students expect the balloons to travel no higher than 500 ft. what distance between the stations would
you recommend? explain.
c. find the heights of balloons sighted with the following angles of elevation to the nearest ten feet. assume a
distance of 500 ft. between stations.
i. 5°, 15°
ii. 38°, 72°
iii. 45°, 45°
iv. 45°, 59°
v. 28°, 44°
vi. 50°, 66°
vii. 17°, 40°
d. based on your results in part (c), which balloon won the contest?
e. the balloons were released several hundred feet away but directly in the middle of the two stations. if the
first angle represents the west station and the second angle represents the east station, what can you say
about the weather conditions during the contest?
f. are there any improvements to mrs. lane’s class’s methods that you would suggest? explain.