Looking up Pablo sees two hot air balloons in the sky as sho

Looking up, Pablo sees two hot air balloons in the sky as shown. He determines that the lower hot air balloon is 670 meters away, at an angle of 42 dgeree from the vertical. The higher hot air balloon is 945 meters away, at an angle of 36 degree from the vertical. How much higher is the balloon on the right than the balloon on the left? Do not round any intermediate computations. Note that the figure below is not drawn to scale.

Solution

To find the difference in their heights,we need to find their heights first

lets find the height of the first triangle or the smaller triangle

Cos 42= adjacent/hypotenuse

cos 42= adjacent/670

Adjacent=670 cos 42

adjacent=497.9m

height of first balloon= 497.9mNext is to find the height of the second balloon

cos 36=adjacent/945

adjacent=945 cos 36

adjacent=764.5 m

height of second balloon=764.5 m

difference in height=764.5-497.9=266.6 m