Answer:
A = 85.87°
B = 124.67 miles
Explanation:
To find the angle of depression, we'll have to know the angle at which the plane makes with vertical height.
See attached document for better illustration.
The plane travels horizontally for 125 miles and it was at a height of 9 miles.
To find the angle of depression, we'll use SOH CAH TOA to know which one suite the question.
SineΘ = opposite / hypothenus
CosΘ = adjacent / hypothenus
tanΘ = opposite / adjacent
The hypothenus is 125 miles and the adjacent is 9 miles. So we can use
CosΘ = adjacent / hypothenus
Cos Θ = 9 / 125
Cos Θ = 0.072
Θ = cos⁻0.072
Θ = 85.87°
The angle of depression which the plane makes is 85.87°
B. The distance the plane travels.
Since we have two side and unknown side in a right angle triangle, we can use pythagorean theorem
X² = y² + z²
X = 125
Y = 9
Z = ?
125² = 9² + z²
Z² = 125² - 9²
Z² = 15544
Z = √(15544)....take the square root of both sides.
Z = 124.67 miles.
The distance of the plane path is 124.67 miles