Question 1139458: Can someone help me with this trigonometry word problem? here goes:
A helicopter maintains an elevation of 3.5 miles and
is flying toward a control tower. The angle of elevation from the
tower to the helicopter is x radians.
Figure: https://i.imgur.com/ncirDGi.png
1. The distance d must be written in miles, between the tower and the heli-copter as a function of x.
2. In this step, d must be found when x = 1 and x = 1.2. Then you must round to the nearest hundredth of a mile.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! here's your diagram.
label the left bottom corner of the triangle A, the top right corner of the triangle B and the bottom right corner of the triangle C.
angle x is at the A corner of the triangle, which is also called angle BAC.
the hypotenuse of the triangle is line segment AB, which we'll call d, because that's the distance from the helicopter to the top of the tower.
the sine of angle x is equal to opposite / hypotenuse which is equal to 3.5 / d.
you get sin(x) = 3.5 / d
solve for d to get d = 3.5 / sin(x)
x apprears to be in radians, so we'll go with that.
when x = 1, you get d = 3.5 / sin(1) = 3.5 / .8414709848 = 4.15938287 miles from the control tower.
when x = 1.2, you get d = 3.5 / sin(1.2) = 3.5 / .932039086 = 3.755207322 miles from the control tower.
the helicopter will be 3.5 miles from the control tower when angle x is equal to pi/2.
you get d = 3.5 / sin(pi/2) = 3.5
that's because the helicopter will be directly above the control tower when x = pi/2.
to convert the angles to degrees, you would multiply the radians by 180 / pi.
1 radian * 180 / pi is equal to 57.29577951 degrees.
1.2 radians * 180 / pi is equal to 68.75493542 degrees.
pi/2 radians * 180 / pi = 90 degrees.
your solutuion, rounded to the nearest hundredth of a mile, will be:
when x = 1, d = 4.16 miles.
when x = 1.2, d = 3.76 miles.
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