A man standing on top of a 100 foot building sites the top of a nearby building at an angle of elevation of 3.14/8. If he knows the nearby building is 160 feet high,what is his horizontal distance from that building.

(3.14/8)/(6.28) * 360 = 22.5o = Angle of elevation.

Tan22.5 = (160-100)/d = 60/d, d = ?.

Note: 3.14/8 Radians = 22.5o.

To solve this problem, we can use trigonometry, specifically the tangent function. The tangent of an angle of elevation is defined as the ratio of the height opposite the angle to the horizontal distance adjacent to the angle.

Let's call the horizontal distance from the man to the nearby building "x". We can set up the following equation using the tangent function:

tan(theta) = opposite/adjacent

In this case, theta is the angle of elevation, which is given as 3.14/8. The opposite side is the height of the nearby building, given as 160 feet. The adjacent side is the horizontal distance, which we want to find.

Plugging these values into the equation, we get:

tan(3.14/8) = 160/x

To solve for x, we can rearrange the equation:

x = 160 / tan(3.14/8)

Now we can calculate the value of x:

x ≈ 640.78 feet

Therefore, the man is approximately 640.78 feet away from the nearby building.