Answer:
Step-by-step explanation:
Given
Balloon in the east makes an angle of elevation of [tex]36^{\circ}[/tex] and is at height of 461 m
Balloon in the west makes an angle of elevation of [tex]51^{\circ}[/tex] 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
[tex]\tan 36=\frac{459.4}{d_1}[/tex]
[tex]\tan 51=\frac{294.4}{d_2}[/tex]
[tex]d_1=632.30 m[/tex]
[tex]d_2=238.4 m[/tex]
Distance between two Balloons
[tex]d=d_1+d_2[/tex]
[tex]d=870.70 m[/tex]
Answer: 777.2m
Step-by-step explanation:
Okay so the work in the answer above is correct but they mixed up the height of the red and blue balloon, so they got the wrong answer.
The red balloon in the east has an angle of 36 degrees and a height of 296.
The blue balloon in the west has an angle of 51 degrees and a height of 461.
Now because Erica is 1.6 meters tall, we will subtract that from the height of both balloons. So the red balloon will have a height of 294.4 and the blue balloon will have a height of 456.4.
Because we are trying to find the distance between the two balloons, we are going to use tan (because tan is opp / adj).
So here’s the trigonometry:
Red:
Tan (36) = 294.4 / a(1)
a(1) = 294.4 / tan (36)
a(1) = 405.2
Blue:
Tan (51) = 459.4 / a(2)
a(2) = 459.4 / tan (51)
a(2) = 372
So the distance is going to be a(1) + a(2) which is 405.2 + 372 = 777.2
So the answer is 777.2m
(Just in case you don’t believe me, this is a homework problem I did for my calculus class and I double checked my answer with the answer key and they are the same. But feel free to check my work :) hope this helps)
