# There is a tunnel which has a maximum depth below ground of 196.9 ft. The downward incline is at an angle of 4.923 degrees. The upward slop is also at an angle of 4.923 degrees to the horizontal. How far apart are the entrances?

##### 1 Answer

The entrances are approximately 4564.947 ft horizontally apart.which is approx.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The tunnel length is approximately 4588.841 feet long.

#### Explanation:

It is often helpful to draw a quick sketch.

Trigonometry is all about ratios. From the diagram the ratio of:

We are given that

So

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

We can use Pythagoras or Trig.

To increase precision I am going to integrate the trig. You will see what I mean as we go along.

From the previous calculation we know that

Substitute for