Question

At a hot air ballon festival, Erica spots a red ballon due east at an angle of elevation of 36 degrees. She turns due west and sees a blue ballon at an angle of elevation of 51 degrees. If the altitude of the blue ballon is 296 meters, the altitude of the blue ballon is 461 meters, and Erica is 1.6 meters tall, find the distance between the balloons.

Answer 1

Answer:

Step-by-step explanation:

Given

Balloon in the east makes an angle of elevation of $36^{\circ}$ and is at height of 461 m

Balloon in the west makes an angle of elevation of $51^{\circ}$ and is at height of 296 m

Erica height is 1.6 m tall   so net altitude of Red balloon is 459.4 m

and net height of Blue balloon is 294.4 m

using trigonometry

$\tan 36=\frac{459.4}{d_1}$

$\tan 51=\frac{294.4}{d_2}$

$d_1=632.30 m$

$d_2=238.4 m$

Distance between two Balloons

$d=d_1+d_2$

$d=870.70 m$