A glider plane is flying between two radar stations which are located 30 miles apart.
The angle of elevation from the radar station to the left of the airplane is 25o and the angle of elevation from the station to the right of the airplane is 18o (Remember to include a sketch). What is the distance between the left radar station and airplane?
To solve this problem, we can create a right triangle with the glider plane as the vertex of the right angle. The two radar stations are the other two vertices of the triangle, and the angles of elevation form the other two angles.
Let x be the distance between the left radar station and the airplane. Then we can set up the following trigonometric equations based on the information given:
tan(25°) = height of airplane / x
tan(18°) = height of airplane / (30 - x)
Solving for the height of the airplane in both equations gives us:
height of airplane = x * tan(25°)
height of airplane = (30 - x) * tan(18°)
Setting these two expressions for the height equal to each other gives:
x * tan(25°) = (30 - x) * tan(18°)
x * 0.4663 = 30 * 0.3249 - x * 0.3249
x * 0.4663 + x * 0.3249 = 30 * 0.3249
0.7912x = 9.7467
x = 9.7467 / 0.7912
x = 12.32 miles
Therefore, the distance between the left radar station and the airplane is approximately 12.32 miles.