A third point C lies on the ground 5.4m from N the angle of depression of C from R is X degrees. Calculate to the nearest degrees the value of X.

My powers of clairvoyance to see the rest of this problem do not seem to be working so well today.

I get atan(|NC|/|NR|) +/- 0.1 deg

To find the value of X, we can use trigonometry, specifically the tangent function.

Let's denote the angle of depression of C from R as X degrees. We know that the distance from N to C is 5.4m. We can consider the right triangle formed by points N, C, and R, with the angle of depression X at point R.

The tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. In this case, we can use the tangent function to relate the angle X to the distance from N to C.

The tangent of X is equal to the height of the triangle (the distance from C to R) divided by the base of the triangle (the distance from N to R).

tan(X) = Height/Base

Now, let's substitute the known values into the equation. The height is the distance from C to R, and the base is the distance from N to R.

Let's say the height is h and the base is b. We have:

tan(X) = h/b

We know that the distance from N to R (base) is equal to the distance from N to C (base) plus the distance from C to R (height). Therefore:

b = 5.4m + h

Substituting this into the previous equation, we get:

tan(X) = h / (5.4m + h)

To solve for X, we can take the inverse tangent (arctan) of both sides of the equation:

X = arctan(h / (5.4m + h))

By plugging in the known values for N and C, we can approximate X to the nearest degree.

Please provide the distance from C to R so that we can calculate the angle X accurately.