Charlie is watching hot air balloons. Balloon A has risen at a 50° angle. Balloon B has risen at a 78° angle. If the distance from balloon A to the ground is 1,000 feet, how far is balloon B from balloon A? Round your answer to the nearest whole number.

(pic in replies)

999 feet
1,005 feet
1,052 feet
1,102 feet

Question

Charlie is watching hot air balloons. Balloon A has risen at a 50° angle. Balloon B has risen at a 78° angle. If the distance from balloon A to the ground is 1,000 feet, how far is balloon B from balloon A? Round your answer to the nearest whole number.

(pic in replies)

999 feet
 1,005 feet
 1,052 feet
 1,102 feet

Kyky232 · Answer

attachment

AZ · Answer

We want to know the distance between balloon B and balloon A

So that means we need to calculate the distance from the ground to Charlie for the first balloon

and then the distance from Charlie to the second balloon

we know that both of them have a height of 1000 meters since they're at the same height in the picture

so let's call those two lengths 'a' and 'b'

AZ · Answer

how would we solve for it?

we have an angle, and the opposite sides
and we want to know the length of the adjacent side

would that be sin, cos, or tan?

Kyky232 · Answer

would that be tan??

Kyky232 · Answer

its opposite over adjacent right?

AZ · Answer

yes, how would you set it up to find the distance from Charlie to balloon A

tan (angle) = opposite / adjacent

Kyky232 · Answer

tan (50)= 1,000/ A  ???

AZ · Answer

Good!

Now solve for A

and remember when you use your calculator that you're in degrees and not radians

Kyky232 · Answer

how would i do that??

Kyky232 · Answer

im not good with the simplifying

AZ · Answer

sure

so we just multiply the A on both sides and we would get

A * tan(50) = 1000

and then divide by tan(50) on both sides so you get A all by itself

AZ · Answer

so basically A = 1000 / tan(50) And you plug it into a calculator https://www.google.com/search?q=1000+%2F+tan(50+degrees)

AZ · Answer

and similarly find B

it's angle is just 78 
and the opposite side is the same 1000

AZ · Answer

and then add up A + B

and that's the distance between them

Kyky232 · Answer

1051.65619285

Kyky232 · Answer

thats what i got

AZ · Answer

that makes two of us https://www.google.com/search?q=1000+%2F+tan(50+degrees)+%2B+1000+%2F+tan(78+degrees) so what's your final answer? just round the number

Kyky232 · Answer

so c?

Kyky232 · Answer

its 1052

AZ · Answer

Yup!!

Kyky232 · Answer

AZ is super smart

AZ · Answer

far from it, but thank you :))

1 attachment

1 attachment