Answer:
1. The angle of descent is:
Rounded to the nearest whole number, the angle of descent is approximately **4 degrees**.
2. The distance of the plane's path is:
hypotenuse
miles
Rounded to the nearest tenth of a mile, the distance of the plane's path is approximately **125.6 miles**.
Step-by-step explanation:
To find the angle of descent and the distance of the plane's path, we will use trigonometric principles.
1. What is the angle of descent?
To calculate the angle of descent, we can use the tangent function, which relates the angle of a right triangle to the ratio of the opposite side to the adjacent side. In this scenario, the vertical drop (opposite side) is 9 miles, and the horizontal distance (adjacent side) is 125 miles. The formula for the tangent of an angle θ is:
opposite
adjacent
We can rearrange this to solve for θ:
opposite
adjacent
Plugging in the values we have:
2. What is the distance of the plane's path?
To find the distance of the plane's path, we will use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. The formula is:
hypotenuse
opposite
adjacent
We can rearrange this to solve for the hypotenuse:
hypotenuse
opposite
adjacent
Plugging in the values we have:
hypotenuse
Now, let's calculate these values.