SOLUTION: The bearing of a house from a point A is 319º. From a point B, 317 m due east of A, the bearing of the house is 288º. How far is the house from A?

Question 1177480: The bearing of a house from a point A is
319º. From a point B, 317 m due east of A,
the bearing of the house is 288º.
How far is the house from A?
Answer by CPhill(1959) (Show Source): You can put this solution on YOUR website!
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.**
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