A tunnel under a river is 196.8 ft below the surface at its lower point. If the angle of depression of the tunnel is 4.962 degrees, then how far apart on the surface are the entrances to the tunnel in feet? I have tan 4.962= 196.8/x but I think I did something wrong?! Thanks
I think you got the distance to the center of the river. Double your x.
To find the distance between the entrances of the tunnel on the surface, we can use the tangent function, as you correctly mentioned. However, it seems like you made a small mistake when setting up the equation.
The angle of depression is the angle between a horizontal line on the surface (parallel to the river) and the line of sight from the surface to the lower point of the tunnel. In this case, the angle of depression is 4.962 degrees.
Let's call the distance between the entrances of the tunnel on the surface "x" (in feet). From the given information, we know that the tunnel is 196.8 ft below the surface at its lower point.
Using the tangent function, we can write:
tan(4.962) = 196.8 / x
Now, let's solve this equation for x.
Begin by isolating x by multiplying both sides of the equation by x:
x * tan(4.962) = 196.8
Next, divide both sides of the equation by tan(4.962):
x = 196.8 / tan(4.962)
Using a calculator, evaluate the right-hand side of the equation:
x ≈ 196.8 / 0.087158
x ≈ 2256.158
Thus, the entrances to the tunnel are approximately 2256.158 feet apart on the surface.