Question

looking up, henry sees two hot air balloons in the sky as shown. 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 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.

Explanation:

Step1: Find height of left balloon

The left balloon's height (vertical component) is \( 515 \times \cos(15^\circ) \) (since adjacent side in right triangle is \( \text{hypotenuse} \times \cos(\theta) \) for vertical angle \( \theta \)).
\( 515 \cos(15^\circ) \approx 515 \times 0.9659258263 \)

Step2: Find height of right balloon

The right balloon's height (vertical component) is \( 840 \times \cos(22^\circ) \) (same logic, adjacent side for \( 22^\circ \) angle).
\( 840 \cos(22^\circ) \approx 840 \times 0.9271838546 \)

Step3: Find the difference

Subtract left height from right height: \( 840 \cos(22^\circ) - 515 \cos(15^\circ) \)
Calculate each term:
\( 840 \times 0.9271838546 \approx 778.8344379 \)
\( 515 \times 0.9659258263 \approx 497.4517005 \)
Difference: \( 778.8344379 - 497.4517005 \approx 281.3827374 \)
Round to nearest tenth: \( 281.4 \)

Answer:

281.4