Altitude The angles of elevation to an air plane from two points A and B on level ground are 71° and 88°,respectively .The points A and B are 5.5 miles apart and the airplaine is east if both points in the same vertical plane. Find the altitude of the plane.
If the plane and the two points are in the same vertical plane, the solution will be:
Calculate the angle formed by the visual lines at the plane point; It will be 180 - 88 - 71 = 21 degrees
According to the sinus law we may write:
5.5(dist between points)/sin 21 = a(opposite to angle A)/ sin 71 = b/sin 88
solving for a and b we obtain:
a = 14.51 miles
b = 15.33 miles
Then we can form tho rectangles triangles, for one the vertical side, forms 90 degrees with the soil then will be the altitude.
Sinus theorem; 14.1/1 = h/sin 88 solving for h = 14.49 miles
To check this answer we can do it in the other triangle:
15.33/1(sin 90) = h/ sin 71, solving for h gives 14.49. so CHECK!!!!!!!!!!!!