bystander at the Pegasus Parade, is lying on his back and observing a large balloon of a cartoon character, floating directly above Broadway Street. He is located 32 feet from a point on the street directly beneath the balloon. To see the top of the balloon, he looks up at an angle of 56°. To see the bottom of the balloon, he looks up at an angle of 46°. To the nearest tenth, how tall, in feet, is the balloon?

Question

bystander at the Pegasus Parade, is lying on his back and observing a large balloon of a cartoon character, floating directly above Broadway Street. He is located 32 feet from a point on the street directly beneath the balloon. To see the top of the balloon, he looks up at an angle of 56°. To see the bottom of the balloon, he looks up at an angle of 46°. To the nearest tenth, how tall, in feet, is the balloon?
any answers on how to set this up

Steve · Answer

Draw a diagram. If the bottom of the balloon is at height x and the top of the balloon is at height y, then

x/32 = tan46°
y/32 = tan56°

The height of the balloon is just y-x, or

32tan56° - 32tan46° = 32(tan56°-tan46°)