Final answer:
Using trigonometry with a given angle of 30° and a height of 100m, the distance of the ship from the port is calculated as 173.2 meters. This is not one of the provided options, but option B could be mistakenly taken as the closest match.
Step-by-step explanation:
To find the distance of the ship from the port of the mountain, we can use trigonometry. The angle of elevation is given as 30°, and the height of the mountain is 100m. To solve this problem, we will use the tangent function, which is the ratio of the opposite side to the adjacent side in a right-angled triangle. This means:
tan(θ) = opposite / adjacent
Here, θ is the angle of elevation (30°), the opposite side is the height of the mountain (100m), and the adjacent side is the distance from the ship to the port, which we are trying to find. So we have:
tan(30°) = 100m / adjacent
Now, since tan(30°) = 1/√3, we can write:
1/√3 = 100m / adjacent
Multiplying both sides by the adjacent side and then by √3 gives us:
adjacent = 100m √3
adjacent = 100m × 1.732
adjacent = 173.2m
Hence, the distance of the ship from the port of the mountain is 173.2 meters, which is not one of the provided options. However, if there was an error in the options, answer option B, 115.5√3 m, would be the closest match after calculating the correct distance.