Question

A ship is 130 m away from the centre of a barrier that measures 180 m from to end. What is the minimum angle that the boat must be turned to avoid hitting the bar

Answer 1

To find the minimum angle, use the tangent function:
`\(\theta = \arctan\left((130)/(90)\right) \approx 54.48^\circ\)`. The boat must turn approximately
`\(54.48^\circ\)`to avoid the barrier.

Let's go through the calculation step by step:

Given:

- Distance from the boat to the center of the barrier r = 130m

- Radius of the barrier R = 90m (half of 180m)

1. Use the Tangent Function:

`\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]`

In this case,
`\(\text{opposite}\)` is the distance from the boat to the center (130m) and
`\(\text{adjacent}\)` is the radius (90m).

`\[ \tan(\theta) = (130)/(90) \]`

2. Find the Inverse Tangent (Arctan):

`\[ \theta = \arctan\left((130)/(90)\right) \]`

3. Calculate the Angle:

Using a calculator to find the arctangent of
`\((130)/(90)\)`, you get:

`\[ \theta \approx 54.48^\circ \]`

Therefore, the boat must turn approximately
`\(54.48^\circ\)` to avoid hitting the barrier.

Que. A ship is 130m away from the center of a barrier that measures 180m from end to end. What is the minimum angle that the boat must be turned to avoid hitting the barrier?