Answer:
Altitude of plane = 390 m
Step-by-step explanation:
The location of the plane, its vertical position on the ground and the takeoff position as displayed in the figure constitute a right triangle with the following dimensions
Hypotenuse c = 890 m
Leg b = 800 m
And we are asked to find the other side )Leg a) which is denoted by the letter x, and represents the vertical height of the plane from the ground
By the Pythagorean Theorem which states the square of the hypotenuse is the sum of the squares of the other two sides we get the generalized formula
[tex]a^{2} + b^{2} = c^{2}[/tex]
where
a = side leg a
b = side leg b
c = hypotenuse
Plugging in c = 890, b = 800 and a = x we get
[tex]x^{2} + 800^{2} = 890^{2}\\\\x^{2} = 890^{2} - 800^{2} \\\\x^{2} = 792100 - 640000\\\\x^{2} = 152100\\\\x = \sqrt{152100}\\\\x = 390 m[/tex]
