Final answer:
To calculate the line of sight and ground distance from the plane to the field for a given angle of depression of 19 degrees and an altitude of 7000 feet, utilize tangent for the ground distance and the Pythagorean theorem for the line of sight distance.
Step-by-step explanation:
To solve this problem, we need to use trigonometry to find both the line of sight distance and the ground distance from the plane to the field. The angle of depression is 19 degrees for a plane flying at 7000 feet above the ground. Let's denote the line of sight distance as L and the ground distance as G.
Firstly, we can consider the situation as a right-angle triangle where the angle of depression corresponds to the angle between the line of sight and the horizontal line. Since we're given the angle of depression and the height (opposite side of the triangle), we can find the adjacent side which is our ground distance G, using the tangent function:
Tan(19°) = Opposite/Adjacent = 7000/G
By rearranging the equation, we get:
G = 7000 / Tan(19°)
Calculate G to find the ground distance.
Next, we can find the line of sight distance L using the Pythagorean theorem:
L² = 7000² + G²
Finally, calculate L to find the line of sight distance.