Question

Alphonse (point A) is over a 2500-meter landing strip in a hot-air
balloon. At one end of the strip, Beatrice (point B) sees Alphonse
with an angle of elevation measuring 39°. At the other end of the strip,
Collette (point C) sees Alphonse with an angle of elevation measuring 62°.
a. What is the distance between Alphonse and Beatrice?
b. What is the distance between Alphonse and Collette?
c. How high up is Alphonse?

Answer 1

You can find angle A. 180 degrees minus (angle B + angle C). Once you have that angle, use the same technique as previous problems.

Answer 2

wait what that support to mean...

Answer 3

how to set the problem with 82

Answer 4

82?

Answer 5

Let D be the point on the earth' s surface directly below the ballon. Let x be AD, the height of the balloon and y be the distance between B and D. Then the two equations below can be derived from the given information:\[\left\{\frac{x}{y}=\text{Tan}[39/180 \pi ],\frac{x}{2500-y}=\text{Tan}[62/180 \pi ]\right\} \]There are two solutions, x and y. Only x is required:
x = 1415.14 and is the answer to question C.

Question A:\[\text{AB}=1415.14\text{ Csc}\left[\frac{13 \pi }{60}\right]=2248.68 \]Question B answer:\[\text{AC}\text{=}1415.14\text{ Csc}\left[\frac{31 \pi }{90}\right]=1602.75 \]

Answer 6

so that mean tan-1(39/180pi)?

Answer 7

what Csc?

Answer 8

OK, Robotey was showing you another way, but I remember you are still in high school. So, as I was saying you don't have angle A. But all triangles are 180, so 180-39-62 would give you A.

Answer 9

you just wonder why 82 because i add 39 and 62 which 101 the subract it then got 79......oop my bad it 79

Answer 10

OK, you know, distance Alphonse and Beatrice is line c, (Sin 62)/c=(Sin 79)/2500

Answer 11

can i crosss it or not

Answer 12

Any way you like, just get c=....

Answer 13

i got 2248.62

Answer 14

Good, same as Robotey, different method.

Answer 15

that would be easy for me

Answer 16

omg this problem took me forever
alot of mistakes lol
i finally got it to work
this is probably the long way

Answer 17

if you want to make fun of me chaguanas,you can

Answer 18

I would, only there is nothing coming up on your attachment. How would you handle the height of Alphonse?

Answer 19

the attachment isn't working? :(

Answer 20

nada

Answer 21

that too hard to rerember this

Answer 22

try again if it doesn't work i will try to explain

Answer 23

Still nothing. Hikari, you got b and c?

Answer 24

the height is the first thing i found...

Answer 25

not really

Answer 26

Distance between Alphonse and collette is line b.
(Sin A)/a=(Sin B)/b

Answer 27

so how i am able to find the angle

Answer 28

You have everything, except line b. So put in all info and solve for b.

Answer 29

so i used the pytagrean thm twice
i called the point that she began her elevation G k?
(this means BG+GC=2500
so we have
AG^2+BG^2=AB^2
AG^2+GC^2=AC^2
solved both of the for AG^2
and set them equal
AB^2-BG^2=AC^2-GC^2
AB^2-AC^2=BG^2-GC^2
AB^2-AC^2=(BG+GC)(BG-GC)
AB^2-AC^2=(2500)(BG-GC)
then i went to the side to get every term in terms of AG
AB=AG/sin39
so
AB^2=AG^2/sin^2(39)
and
AC=AG/sin62
so
AC^2=AG^2/sin^2(62)
also
BG=AG/tan39
and
GC=AG/tan62
then i got
\[AG^2(\frac{1}{\sin^239}-\frac{1}{\sin^2(62)})-AG(2500)(\frac{1}{\tan39}-\frac{1}{\tan62})=0\]

Answer 30

So AG cannot be zero so
AG=1415.142464

Answer 31

so i am still using 39 and 62

Answer 32

the rest easy
AC=1415.142464/sin62
AB=1415.142464/sin39

Answer 33

Yes, Hikari. Wow, Myininaya, a lot of work.

Answer 34

yes u know
thats why i was hoping the attachment would work lol

Answer 35

i have three other attemps like this but they are in the garbage because i kept making an error then finally PERFECTO! lol

Answer 36

Great. Now if we can find the elementary method to show hikari.

Answer 37

now i know c is 2248.7 so i can use that

Answer 38

i think my way is elementary but long
However I think the problem could have been solved with less steps

Answer 39

Yes, Hikari, you can use c if you like.

Answer 40

so sin62/B=sin39/2248.7

Answer 41

Mix up
(Sin 39)/b=(Sin 62)/2248.7

Answer 42

and then with that fix you will have the same answer as rob and i

Answer 43

i think you have one more leg remaining that you need to find the length
do you know law of cosines?

Answer 44

i got 1602.79 so can i round it or not

Answer 45

i assume rounding is okay i believe it is impossible to have the exact value anyways

Answer 46

so now the c question

Answer 47

Ok, if you draw a line from A to bottom, it makes a right angle. So you can use sin.
Sin B=Alphonseheight/2248.7. Solve for Alphonse height.

Answer 48

sinB=A/2248.7

Answer 49

sinB=A/2248.7

Answer 50

Yeah, but call it something else don't call it A. Let's call it p.
Sin 39=p/2248.7

Answer 51

i got 1415.10

Answer 52

Good! Same thing Myinaya have. Good job.

Answer 53

gj hirkari

Answer 54

thank for helping me and esay for me to remember this thank you

Answer 55

:)