If an airplane covered 13 miles of its route while decreasing its altitude by 42,000 feet.?

Question

If an airplane covered 13 miles of its route while decreasing its altitude by 42,000 feet. Find the slope of the airplane's line d to the nearest hundredth. [Hint: 1 mi = 5280 feet.]

can someone help me please?

Answer 1

Assume the earth is relatively flat over the 13 miles covered by the airplane. The 13 miles of its route is the horizontal distance covered, not the slope distance as is decreases altitude. Draw a diagram by starting with a 13 mile horizontal line on the earth's surface. At the left end of the line draw a vertical line upwards and label it 42,000 feet. Label the 13 mile horizontal line 13 x 5280 to change it to feet. Now slope is the ration of rise to run, or in this case drop to run (drop or fall is negative) so the airplane's slove as it descends is

slope = drop/run = -42000/(13x5280) = 0.61. This means the airplane is dropping vertically 0.61 feet(or miles) or each foot (or mile) traveled horizontally. This is the change of vertical distance per unit change in horizontal distance which you will study in detail in calculus.

Answer 2

It is a ratio firstly that can be converted into a angle (negative).
=42000/(13*5280)
=42000/68640
=0.611888111 (slope)

converted to degree is -35.0586 degrees

If it was 45 degrees height and distance would be the same, as the plane covered more distance than lost height the angle is less than 45 degrees, and since the plane is descending it is a negative value.

Answer 3

Assuming the 13 miles is the horizontal of a right angled triangle.
vertical distance = 42,000ft = 7.95 miles
tan θ = 7.95 / 13
tan θ = 0.61
slope, m = 0.61

Answer 4

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