An airplane takes off from an airport. When the airplane reaches a height of 16,500 (ft), the airplane has traveled a horizontal distance of 6000 ft, as shown in the diagram below.
+9479 Part A:
tan( x ) = opposite / adjacent
tan( x ) = 16500 / 6000
tan( x ) = 11/4
x = arctan( 11/4 )
x ≈ 70°
Part B:
This is the length of the third/unknown side of the triangle, which we can find using the Pythagorean Theorem. Let's call this side "c". Then...
60002 + 165002 = c2
\(\color{} c\ =\ \sqrt{6000^2+16500^2}\)
We could plug the above into a calculator, or we can first simplify it like this before plugging it in:
\(\color{gray} c\ =\ \sqrt{6000^2+16500^2} \\~\\ \color{gray} c\ =\ \sqrt{(4\cdot1500)^2+(11\cdot1500)^2} \\~\\ \color{gray} c\ =\ \sqrt{4^2\cdot1500^2+11^2\cdot1500^2} \\~\\ \color{gray} c\ =\ \sqrt{1500^2(4^2+11^2)} \\~\\ \color{gray} c\ =\ \sqrt{1500^2}\cdot\sqrt{(4^2+11^2)} \\~\\ \color{gray}c\ =\ 1500\sqrt{137} \)
Now if we put this into a calculator we get:
c ≈ 17557 (And this is in feet)
