Looking up, Chang sees two hot air balloons in the sky as shown. He determines that the lower hot air balloon is 810 meters away, at an angle of $19^{\circ}$ from the vertical. The higher hot air balloon is 935 meters away, at an angle of $15^{\circ}$ from the vertical. How much higher is the balloon on the right than the balloon on the left?
Do not round any intermediate computations. Round your answer to the nearest tenth.
Note that the figure below is not drawn to scale.

Step 1 ：Given that the lower hot air balloon is 810 meters away, at an angle of $19^{\circ}$ from the vertical, and the higher hot air balloon is 935 meters away, at an angle of $15^{\circ}$ from the vertical.

Step 2 ：We can use the cosine function to calculate the height of each balloon from Chang's position. The height of the balloon is the adjacent side of the triangle formed by Chang, the balloon, and the vertical line from Chang to the balloon. The cosine of the angle is equal to the adjacent side (height of the balloon) divided by the hypotenuse (distance to the balloon). So, the height of the balloon is equal to the cosine of the angle times the distance to the balloon.

Step 3 ：First, we convert the angles from degrees to radians. The angle of the lower balloon in radians is approximately 0.3316 and the angle of the higher balloon in radians is approximately 0.2618.

Step 4 ：Next, we calculate the height of each balloon. The height of the lower balloon is approximately 765.87 meters and the height of the higher balloon is approximately 903.14 meters.

Step 5 ：Finally, we subtract the height of the lower balloon from the height of the higher balloon to find the difference in height. The difference in height is approximately 137.27 meters.

Step 6 ：Rounding to the nearest tenth, we find that the balloon on the right is \(\boxed{137.3}\) meters higher than the balloon on the left.