Question 1177480
Let's break down this problem step by step.

**1. Visualize the Situation**

Draw a diagram to represent the given information.

* Label point A and point B, with B being 317 m due east of A.
* Mark the bearings of the house from A and B as 319° and 288°, respectively.
* Let H represent the location of the house.

**2. Identify the Angles**

* Since bearings are measured clockwise from north, angle NAB = 360° - 319° = 41°.
* Similarly, angle ABH = 360° - 288° = 72°.
* In triangle ABH, angle AHB = 180° - 41° - 72° = 67°.

**3. Apply the Law of Sines**

We can use the Law of Sines to find the distance AH (the distance from the house to point A):

```
AH / sin(ABH) = AB / sin(AHB)
```

Plugging in the values:

```
AH / sin(72°) = 317 / sin(67°)
```

Solving for AH:

```
AH = 317 * sin(72°) / sin(67°)
AH ≈ 328.4 m
```

**Therefore, the house is approximately 328.4 meters away from point A.**