Question

You are riding in a hot-air balloon over the African savanna when you look down along a 32° angle of depression and spot a lion that is 220 meters away diagonally from your position in the balloon.



Part A (7 points): Write a trigonometric equation that can be used to determine the altitude of your balloon.



Part B (9 points): Solve your equation from Part A to determine the altitude of your balloon. Round to the nearest meter.



Part C (9 points): Your altitude remains the same, but you move toward the lion’s position until the lion is 190 meters away diagonally from your position in the balloon. Determine the land distance the balloon is from the lion. Round to the nearest meter.

Answer 1

Part A:

Let h be the altitude of the balloon.

Using the trigonometric relationship, we have:

tan 32° = h / 220

Part B:

tan 32° = h / 220
h = 220 * tan 32°
h ≈ 135 meters

Therefore, the altitude of the balloon is approximately 135 meters.

Part C:

Let x be the land distance the balloon is from the lion when the lion is 190 meters away diagonally.

Using the trigonometric relationship again, we have:

tan 32° = h / x
x = h / tan 32°
x ≈ 251 meters

Therefore, the land distance the balloon is from the lion when the lion is 190 meters away diagonally is approximately 251 meters.