Question

Looking up, Maya sees two hot air balloons in the sky shown. She determines that the lower hot air balloon is 425 meters away, at an angle of 31 degrees from the vertical. The higher hot air balloon is 560 meters away, at an angle of 43 degrees from the vertical. How much higher is the balloon on the right than the balloon on the left?

A. 105 meters

B. 135 meters

C. 155 meters

D. 175 meters

Answer 1

The balloon on the right is approximately 167.05 meters higher than the balloon on the left.

Step-by-step explanation:

To find how much higher the balloon on the right is compared to the balloon on the left, we need to consider the vertical component of their distances. The vertical component of the distance is given by the distance multiplied by the sine of the angle. For the lower balloon, the vertical distance is 425 meters * sin(31°) = 217.93 meters. For the higher balloon, the vertical distance is 560 meters * sin(43°) = 384.98 meters. The difference between these two vertical distances is 384.98 meters - 217.93 meters = 167.05 meters.

Therefore, the balloon on the right is approximately 167.05 meters higher than the balloon on the left.