Question

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

Please show workings and a diagram.​

Answer 1

• 190.2 m

Explanation:

Refer to diagram in the attachment (not drawn to scale)

A and B are mentioned points and H is the home location.

Bearing on AH is 319°, the angle between horizontal line and AH is:

• 319° - 270° = 49°

Bearing on ABH is 288°, the angle between horizontal line and BH is:

• 288° - 270° = 18°

The 49° is the exterior angle, so the angle H is:

• 49° - 18° = 31°

Use the law of sines to find x, the distance AH:

• x/sin 18° = 317/sin 31°
• x = 317 sin18° / sin 31°
• x = 190.2 m (rounded)