Answer:
Without knowing the actual distances involved, it's difficult to give a specific answer. However, we can use the information given in the question to determine the distance between points A and C using the Pythagorean theorem.
Let's assume that the boy walked a distance of x units from point A to point B, and a distance of y units from point B to point C. Then we can use the following diagram:
C
|
y |
| | x
|-----------B
|
|
A
According to the problem, the boy first walked a certain distance x in a direction that is not specified (we only know that it's forward and north). Then he turned 136 degrees to his right and walked a distance y to reach point C. Since the turn was to the right, the boy turned towards the east, so we can draw a line from point B towards the right to represent this change in direction.
Now we can apply the Pythagorean theorem to find the distance between points A and C:
AC² = AB² + BC²
We know that AB = x, and we need to find BC. To do so, we can use trigonometry. Since the boy turned 136 degrees to his right, he ended up facing 180 - 136 = 44 degrees east of north. This means that the angle between BC and AB is 90 - 44 = 46 degrees.
Using trigonometry, we can express BC in terms of y and the tangent of the angle 46 degrees:
tan(46) = BC / y
BC = y tan(46)
Substituting this expression for BC into the Pythagorean theorem equation, we get:
AC² = x² + (y tan(46))²
Simplifying:
AC² = x² + y² tan²(46)
We can calculate tan²(46) using a calculator or a table of trigonometric functions. Let's assume that tan²(46) is equal to 1.470. Then we have:
AC² = x² + 1.470y²
To find the distance between A and C, we need to take the square root of both sides of the equation:
AC = sqrt(x² + 1.470y²)
Without more information about the distances involved, we cannot compute the actual numerical value of AC.