in the distance you see an arch 192 meters high, you estimate your line of sight with the top of the arch to be 8.4 degree. appox how far in kilometers are you from the base of the arch?

tan 8.4 = 0.192/d

To find the approximate distance from the base of the arch, we can use trigonometry. We'll use the tangent function (tan) in this case.

First, convert the 8.4 degrees to radians by multiplying it by π/180:

8.4 * (π/180) = 0.1464 radians (approximately)

Now, we can set up the equation:

tan(angle) = opposite / adjacent

In this case, the opposite side is the height of the arch (192 meters) and the adjacent side is the distance we want to find.

tan(0.1464) = 192 / distance

Now, solve for distance:

distance = 192 / tan(0.1464)

Using a calculator, we find that tan(0.1464) is approximately 0.002554.

distance = 192 / 0.002554

distance ≈ 75,119.91 meters ≈ 75.12 kilometers

So, you are approximately 75.12 kilometers from the base of the arch.