To find the distance between the boat's starting point and its current position, we can use the Law of Cosines.
Let's call the starting point O, the point after sailing 4km A, and the point after sailing 5km B.
Using the given bearings, we can draw a triangle with side lengths 4km, 5km, and an unknown side x (the distance from the starting point to the current position of the boat).
By drawing a sketch, we can also observe that the angle between the known sides of length 4km and 5km is (67 degrees - 38 degrees) = 29 degrees.
Applying the Law of Cosines:
x² = 4² + 5² - 2 * 4 * 5 * cos(29°)
x² = 16 + 25 - 40 * cos(29°)
x² = 41 - 40 * cos(29°)
x² = 41 - 40 * 0.875
x² = 41 - 35
x² = 6
Taking the square root of both sides:
x = √6
Therefore, the boat is approximately √6 km away from its starting point.
To calculate the bearing of the boat from its starting point, we can use the Law of Sines.
Using the same triangle formed by points O, A, and B:
sin(29°) / x = sin(α) / 5
Where α is the angle between the known side of length 5km and the unknown side of length x.
Simplifying the equation:
sin(α) = (5 * sin(29°)) / √6
sin(α) = 3.532 / 2.449
sin(α) ≈ 1.441
Since sin(α) is positive, the angle α is in the first quadrant. Thus, the bearing of the boat from its starting point is given by:
α ≈ arcsin(1.441) = 88.169 degrees
Therefore, the boat is approximately √6 km away from its starting point, and its bearing from the starting point is approximately 88.169 degrees.
A boat sails 4km on a bearing 038 degrees and then 5km on a bearing of 067 degree how far is the boat from its starting point and calculate the bearing of the boat from its starting point
1 answer
1 answer