Answer:
5471 feet
Step-by-step explanation:
To find the distance the plane has flown (AB (c)), we can use trigonometric ratios.
Since we have the opposite side (BC) and we want to find the hypotenuse (AB), we'll use the sine function.
Given:
Angle of elevation, [tex] A = 10^\circ [/tex]
Opposite side, [tex] BC = 950 [/tex] ft
Using the sine function:
[tex] \sin(A) = \dfrac{{\textsf{opposite}}}{{\textsf{hypotenuse}}} [/tex]
Substitute the value:
[tex] \sin(10^\circ) = \dfrac{{BC}}{{AB}} [/tex]
[tex] \sin(10^\circ) = \dfrac{{950}}{{c}} [/tex]
We need to solve for [tex] (c) [/tex].
Rearranging the equation, we get:
[tex] c = \dfrac{{BC}}{{\sin(A)}} [/tex]
Now we can substitute the given values and calculate:
[tex] AB = \dfrac{{950}}{{\sin(10^\circ)}} [/tex]
Using a calculator, find the value of [tex]\sin(10^\circ)[/tex], then divide 950 by that value.
[tex] AB = \dfrac{{950}}{{\sin(10^\circ)}} \\\\ \approx \dfrac{{950}}{{0.1736481777}} \\\\ \approx 5470.831956 \\\\ \approx 5471 \textsf{ ft ( in nearest foot)}[/tex]
So, the plane has flown approximately 5471 feet.
