Question

Assume that all triangles have interior angles less than 90°.A surveyor sights on a survey marker that is 132.3m distant. She needed to turn her transit (her survey instrument) 75° to sight on a second survey marker. She knows that from the second marker, the angle between the line of site from her own position and the first marker is 68°. How far is she from the second marker?​

Answer 1

85.9 m

Explanation:

The law of sines can help figure this.

The remaining angle in the triangle is ...

180° -75° -68° = 37°

This is the angle opposite the leg from the surveyor to the second marker. Referencing the attachment, we have ...

b/sin(B) = c/sin(C)

b = sin(B)·c/sin(C) = 132.3·sin(37°)/sin(68°) ≈ 85.873 . . . meters

The surveyor is about 85.9 meters from the second marker.