Answer:
shortened height = h(1 - tan(20))
Explanation:
To solve this problem, we need to use trigonometry to find the height that the airplane reaches at a 20° angle, and then subtract this height from the height of the cell tower to determine how short it needs to be.
Let's assume that the cell tower has a height of "h", and that the airplane takes off at a 20° angle. We can use trigonometry to find the height "x" that the airplane reaches above the ground:
tan(20) = x / h
Multiplying both sides by "h", we get:
x = h * tan(20)
So the airplane reaches a height of "x" above the ground. To find how short the cell tower needs to be, we simply subtract this height from the original height of the tower "h":
shortened height = h - x
Substituting the expression we found for "x", we get:
shortened height = h - h * tan(20)
Simplifying, we get:
shortened height = h(1 - tan(20))
So, the cell tower needs to be shortened by "h(1 - tan(20))" to ensure that the airplane can take off safely at a 20° angle.