Answer:
We can use trigonometry to solve this problem. Let's call the distance from point A to the boat "x" and the distance from point B to the boat "y". Then we have:
In triangle AOC, tan(12) = OC / x
In triangle BOC, tan(64) = OC / y
We want to find the distance from point A to point B, which is the difference between x and y:
Distance AB = y - x
To solve for x and y, we need to eliminate OC. We can do this by setting the two expressions for OC equal to each other and solving for OC:
tan(12) = OC / x
OC = x tan(12)
tan(64) = OC / y
OC = y tan(64)
x tan(12) = y tan(64)
y = x tan(12) / tan(64)
Now we can substitute this expression for y into the equation for Distance AB:
Distance AB = y - x
Distance AB = x tan(12) / tan(64) - x
We can simplify this expression by factoring out an x:
Distance AB = x (tan(12) / tan(64) - 1)
Now we just need to plug in the values and calculate:
Distance AB = x (0.2174 - 1)
Distance AB = -0.7826 x
Since distance cannot be negative, we know that x > 0. Therefore, the boat is between point A and point B, and the distance from point A to point B is:
Distance AB = x (0.2174 - 1)
Distance AB = -0.7826 x
Distance AB ≈ 1.28 x
We don't know the actual value of x, but we can see that the distance from point A to point B is approximately 1.28 times the distance from point A to the boat when Jaxson measured the angle of depression to be 12 degrees.
Explanation: