On a banked race track, the smallest circular path on which cars can move has a radius of 117 m, while the largest has a radius 167 m, as the drawing illustrates. The height of the outer wall is 18 m.
To find the height of the inner wall of the banked race track, we can use the concept of similar triangles.
First, let's denote the height of the inner wall as "h". We can form a right triangle with one side as the radius of the inner path (117 m) and the other side as the difference in radii between the outer and inner paths (167 m - 117 m = 50 m).
Now, in this right triangle, we can see that the ratio of the height h to the difference in radii (50 m) is equal to the ratio of the height of the outer wall (18 m) to the difference in radii (50 m).
So, we have the equation: h / 50 m = 18 m / 50 m.
To find the value of h, we can cross-multiply and solve for h.
h = (18 m * 50 m) / 50 m
Canceling out the units of meters, we have:
h = 18 m.
Therefore, the height of the inner wall of the banked race track is 18m.