a balloon can be seen from two observations posts. From A, the angle of the elevation is 30degree and from B, it is 45degree. If the balloon is 1000m high, what is the maximum possible distance between A and B?
pls. help me what to do...
2007-02-11 22:43:03 · 3 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
use the rules of 45,45,90 and 30,60,90 triangles. if you know the balloon is 1000 meters in the air this is a side of both triangles. for the 45,45,90 triangle this distance is equal to the distance of the observer to directly underneath the balloon on the ground. for the 30,60,90 triangle multiply 1000m by the square root of three to get 1732.05. if you add these distances together this is the the max distance between A and B.
roughly 2732.05meters
2007-02-11 22:52:34 · answer #1 · answered by stud muffin 2 · 0⤊ 0⤋
You can set up a graphical solution. Assume that A and B are two points on a horizontal level ground in a line. From A the balloon is at an angle of 30 degrees and from B the balloon makes an angle of 45 degrees. So, B is closer to the point C where the balloon is tethered, assuming that the balloon is straight up vertically. And assume that the position of the balloon is given by point O. So, now you have two triangles, AOC and BOC. You can work out the distance between A and B if you use a scaled graph. It is possible to do it mathematically also. Here are the steps for the maths:
OC / AO = tan 30 and OC / BO = tan 45; we know tan 45 = 1
So OC = BO = 1000 m
Substituting in the first relationship, we have 1000 / AO = tan 30
AO = 1000 / tan 30 = 1732.05 m
So, the distance between A and B could be 732 m approx.
2007-02-12 07:06:10 · answer #2 · answered by Swamy 7 · 0⤊ 0⤋
the distance is 2000multiply by root3
process
the angle of elevation of A is 30degree then tan30=1000/o(let the foot of balloon is o)=1000 root3.
do the same with tan45
then add the both u will get the answer
2007-02-12 08:01:26 · answer #3 · answered by kanni 1 · 0⤊ 0⤋