A jet plane flying 6000 m above the ground passed directly above Ana. one minute later, Ana noticed that the plane's angle of elevation was 18 degrees 34 minutes. What was the horizontal distance covered by the plane?

Question

A jet plane flying 6000 m above the ground passed directly above Ana. one minute later, Ana noticed that the plane's angle of elevation was 18 degrees 34 minutes. What was the horizontal distance covered by the plane?

Answer 1

6000/x = tan 18°34'

just solve for x

Answer 2

To find the horizontal distance covered by the plane, we can use trigonometry. We'll start by drawing a diagram to visualize the situation.

Let's assume that Ana is standing at point A on the ground, directly below the plane. We'll also label the point where Ana noticed the plane's angle of elevation as point B. The angle of elevation is the angle formed between Ana's line of sight to the plane and the horizontal line.

Now, let's label the height of the plane above the ground as h = 6000 m and the horizontal distance covered by the plane as x (which is what we need to find).

From the diagram, we can form a right-angled triangle ABC, where:
- Side AB represents the height of the plane (h = 6000 m).
- Side BC represents the horizontal distance covered by the plane (x).
- The angle at B is the angle of elevation (18 degrees 34 minutes).

To use trigonometry, we need to convert the angle of elevation from degrees and minutes to decimal degrees. 1 degree = 60 minutes, so we can convert 34 minutes to decimal form by dividing it by 60: 34/60 = 0.567 degrees.

Now, we have an angle of elevation of 18 degrees 0.567 degrees.

Using trigonometry, the tangent of the angle of elevation can be calculated as follows:
tan(angle) = opposite/adjacent
tan(18.567) = h/x

Rearranging the equation to solve for x, we get:
x = h / tan(angle)

Now we can substitute the given values:
x = 6000 / tan(18.567)

Using a scientific calculator or an online tool, we can calculate the value of tan(18.567) to be approximately 0.3259.

Substituting this value into the equation, we find:
x = 6000 / 0.3259

Evaluating the expression, we find that the horizontal distance covered by the plane is approximately 18409.7 meters (rounded to one decimal place).

Therefore, the horizontal distance covered by the plane is approximately 18409.7 meters.