SOLUTION: Hi, I was hoping you can help me on this: Two students standing 3000M apart see the same airplane flying in the sky between them. Student A measures the angle of elevation to be

Algebra ->  Trigonometry-basics -> SOLUTION: Hi, I was hoping you can help me on this: Two students standing 3000M apart see the same airplane flying in the sky between them. Student A measures the angle of elevation to be      Log On


   

Question 204821: Hi, I was hoping you can help me on this:
Two students standing 3000M apart see the same airplane flying in the sky between them. Student A measures the angle of elevation to be 37 degrees. Student B measures the angle of elevation to be 30 degrees. How high is the airplane.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Two students standing 3000M apart see the same airplane flying in the sky between them.
Student A measures the angle of elevation to be 37 degrees.
Student B measures the angle of elevation to be 30 degrees.
How high is the airplane.
:
Find the 3rd angle of the triangle formed by the plane and the two observers:
180 - 37 - 30 = 113 degrees
:
Find the side (a) opposite the 37 degree angle using the law of sines
sin%28113%29%2F3000 + sin%2837%29%2Fa
Find the sines and cross multiply
.9502a = 3000 * .6018
.9502a = 1805.445
a = 1805.445%2F.9502
a = 1961.364
:
Drop a line from the 113 degree angle and perpendicular to the base,
this is the altitude of the plane
;
This forms two right angle triangles, use the one containing the angle of 30 degrees
Find the altitude (h) using the sine of 30 degrees:
Sin(30) = h%2F1961.364}
.5 = h%2F1961.364}
h = .5 * 1961.346
h = 980.673 meters is the height of the plane