A hot air balloon is tethered to the ground with a 30 meter rope. Find the altitude of the balloon, when the rope makes a 60 degree angle with the ground.
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 Mr. Alaa'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 𝜶 and 𝜷 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.
a. 𝟓°, 𝟏𝟓°
b. 𝟑𝟖°, 𝟕𝟐°
c. 𝟒𝟓°, 𝟒𝟓°
d. 𝟒𝟓°, 𝟓𝟗°
e. 𝟐𝟖°, 𝟒𝟒°
f. 𝟓𝟎°, 𝟔𝟔°
g. 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 Mr. Alas class’s methods that you would suggest? Explain.