Complete question :
The distance from town X to town Y is 200 km. The distance from town X to town Z is 135 km. Looking from town Y, town X and town Z are separated by an angle of 42°. Sketch possible diagrams for this situation. Calculate the possible distances from town Y to town Z.
Answer:
166 km
Explanation:
Given that :
X to Y = 200km
X to Z = 135 km
X and Z are separated by 42°
Using Sine rule :
x
z / sinZ = y / sinY
200/ sinZ = 135/sin42
SinZ = (200 * sin42) / 135
SinZ = 0.9913046
Sin^-1 (0.9913)
Z = 82.438
Z = 82.44
Hence,
X = 180 - (Z + Y) (angles in a triangle)
X = 180 - (82.44 + 42)
X = 55.56°
To obtain x:
x / sin X = y / sin Y
x / sin 55.56 = 135 / sin 42
x * sin 42 = sin 55.56 * 135
x = (55.56 * 135) / sin42
x = 111.33704 / 0.6691306
x = 166.39059
Hence, possible Distance from town Y to town Z= 166 km