Question

A portion of a roller coaster track is shown in the figure above. the roller coaster track is shown at ground level at point S and travels in a stright line up a 23 degree incline befire reaching its biggest point X, which is 78.4 feet above ground level. what is the distance in feet that the rollercoaster travels to point X?

Answer 1

Answer:

Step-by-step explanation:

This is classic right triangle trig.  The height of the hill is 78.4 which serves as the side opposite the reference angle of 23 degrees.  The side we are looking for is the hypotenuse of that triangle.  The trig ratio that relates the side opposite a reference angle to the hypotenuse of the right triangle is the sin ratio.  Setting it up using our values:

$sin(23)=\frac{78.4}{x}$, where x is the unknown length of the hypotenuse.  Solving for x:

$x=\frac{78.4}{sin(23)}$

Make sure your calculator is in degree mode before entering this in.  You will get a length of the hypotenuse as 200.649 feet, so choice A.