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

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.

166 km

Step-by-step 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

there is no