Question

Looking up, Carlos sees two hot air balloons in the sky. He determines that the lower hot air balloon is 515 meters away, at an angle of 15° from the vertical. The higher hot air balloon is 840 meters away at an angle of 22° from the vertical. How much higher is the balloon on the right from the balloon on the left? Do not round any intermediate computations. Round your final answer to the nearest tenth.

A) 175.0 meters
B) 325.0 meters
C) 313.7 meters
D) 215.0 meters

Answer 1

The difference in height between the two balloons is determined by using trigonometry to calculate the height of each separately and then finding the difference between the two. After performing the calculations, the higher balloon is 313.7 meters above the lower one when the final answer is rounded to the nearest tenth.

Step-by-step explanation:

The student asks how much higher the second balloon is compared to the first, given their distances from Carlos and the angles from the vertical. To find the height difference, we use trigonometry. For each balloon, the height can be found by calculating the opposite side of a right triangle, with the distance given as the hypotenuse and the angle provided from the vertical.

For the lower balloon, the height (h1) is:

• h1 = 515 * sin(15°)

For the higher balloon, the height (h2) is:

• h2 = 840 * sin(22°)

The difference in height (Δh) is the height of the second balloon minus the height of the first balloon:

• Δh = h2 - h1

After calculating, we round the final answer to the nearest tenth to find option C) 313.7 meters as the correct answer.