a plane is one mile above sea level when it begins to climb at a constant angle of 3 degrees for the next 60 ground miles. about how far above sea level is the plane after its climb

Question

a plane is one mile above sea level when it begins to climb at a constant angle of 3 degrees for the next 60 ground miles. about how far above sea level is the plane after its climb

Answer 1

You need to draw right triangle ABC.

Angle A (vertex angle) = 3 deg
side b (base) = 60 mi
side c = hypotenuse
side a (distance of climb) = unknown

tan A = op/hyp = a/b = a/60
tan 3 = a/60
0.0524 = a/60
60(0.0524) = a
3.144 mi = a

So the plane climbed 3.144 miles
To find how far above sea level after the climb,

1 mile + 3.144 miles = 4.144 miles above sea level

Answer 2

To calculate the distance above sea level after the plane's climb, we can use trigonometry. The angle of climb is 3 degrees, and the ground distance covered during the climb is 60 miles.

We can start by calculating the vertical distance climbed (d1) using the formula:

d1 = distance * sin(angle)

Substituting the values, we have:

d1 = 60 * sin(3 degrees)

Using a calculator, we find that sin(3 degrees) is approximately 0.05234. Therefore,

d1 = 60 * 0.05234 = 3.1404 miles

So, the plane has climbed approximately 3.1404 miles above sea level after its climb.

Answer 3

To determine how far above sea level the plane is after its climb, we need to calculate the vertical distance it has traveled during the climb.

First, let's calculate the vertical distance the plane travels per mile horizontally. We can use basic trigonometry to find the vertical component of the climb angle.

The vertical component of the climb angle can be calculated using the formula:

Vertical distance per mile = horizontal distance per mile × tan(angle)

Given that the angle is 3 degrees and the horizontal distance per mile is 1, we can calculate the vertical distance per mile:

Vertical distance per mile = 1 × tan(3°)

Using a scientific calculator, we find that tan(3°) is approximately 0.0524. So:

Vertical distance per mile ≈ 1 × 0.0524 ≈ 0.0524 miles

Now, to find the vertical distance traveled during the climb, we multiply the vertical distance per mile by the total ground miles of the climb. In this case, the climb is for 60 ground miles:

Vertical distance traveled during the climb = vertical distance per mile × ground miles of climb

Vertical distance traveled during the climb = 0.0524 miles/mile × 60 miles

Vertical distance traveled during the climb ≈ 3.144 miles

Therefore, the plane is approximately 3.144 miles above sea level after its climb.