From two different tracking stations, a weather balloon is spotted from two angles of elevation, 57degrees and 83 degrees, respectively. The tracking stations are 15 km apart. Find that altitude of the balloon.
Any help given will be greatly appriciated
Sonia, check the angles and make sure
they are the same as those posted.
Oh sorry this is right, I read the wrong answer, thank u for your help:)
I didn't get the labeling! Like what is h ?
Solve for X:
(X +15)*1.54 = 8.14X
1.54X + 23.1 = 8.14X
X = 3,5km
Please show more details on solving for x
To find the altitude of the balloon, we can use the concept of trigonometry and the properties of angles of elevation.
Let's assume that the altitude of the balloon is represented by "h".
We have two angles of elevation, one from each tracking station, which are 57 degrees and 83 degrees, respectively.
Now, let's consider the triangle formed by the balloon's altitude (h), the distance between the tracking stations (15 km), and the line connecting the two tracking stations.
We can label the triangle as follows:
tracking station A
/ \
/ \
/ \
/ \
/h \
/_________________________\
tracking station B line connecting the tracking stations
Within this triangle, the sides opposite the angles of elevation will be equal to the altitude of the balloon (h). Therefore, we can create two right-angled triangles with the following side lengths:
Triangle 1:
Adjacent Side: 15 km (distance between the tracking stations)
Opposite Side: h (altitude of the balloon)
Angle of Elevation: 57 degrees
Triangle 2:
Adjacent Side: 15 km (distance between the tracking stations)
Opposite Side: h (altitude of the balloon)
Angle of Elevation: 83 degrees
Now, to find the value of h (altitude), we can make use of the trigonometric function called tangent (tan).
In Triangle 1, the equation using tangent can be written as:
tan(57 degrees) = h / 15 km
In Triangle 2, the equation using tangent can be written as:
tan(83 degrees) = h / 15 km
To solve for h, we can rearrange both equations:
For Triangle 1:
h = 15 km * tan(57 degrees)
For Triangle 2:
h = 15 km * tan(83 degrees)
Now, let's calculate the value of h using the given equations:
For Triangle 1:
h = 15 km * tan(57 degrees) ≈ 21.33 km
For Triangle 2:
h = 15 km * tan(83 degrees) ≈ 85.84 km
Therefore, the altitude of the balloon is approximately 21.33 km, based on the calculations from the given angles of elevation.
First, I'm going to give you
instructions and INFO for drawing
a picture of the problem. The picture
is the key to understanding the
problem. So it has to be drawn correctly.
1. Draw a horizontal line. 2. At the left end, draw a vertical line upward
to form a rt. angle. 3. Draw a hypotenuse from the top of vertical
line to rt. end of the horizontal
line. 4. Label the acute angle between
hyp. and the horizontal 57 deg.
5. Draw a 2nd hyp. from the top of
vertical line to horizontal line at
a point greater than half way to left
end. Label the acute angle formed
83 deg. 6. The distance between the
2 hyp. should be labeled 15km on the
hor. line.Label the remaining distance
X on hor. line. The total hor. dist.
= X + 15. 7. Label vertical line h.
Tan57 = h / (X+15), h = ( x + 15)7an57.
Tan 83 = h/X, h = X Tan83.
h = (X +15) Tan 57 = X Tan 83.
Solve for X:
(X +15)*1.54 = 8.14X
1.54X + 23.1 = 8.14X
X = 3,5km
h = X Tan 83 = 3.5 * 8.14 = 28.5km.=
Altitude.