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

x = 10.1

step-by-step explanation:

all of the angles of a tirangle add up to 180º

180 - 65 = 115 (since we already know the value of one angle)

(2x + 7) + (8x + 7) = 115

(combins like terms) 10x + 14 = 115

(isolate the variable subtract 14 from both sides): 10x = 101

(find the variable divide both sides by 10): x = 101/10

x = 10.1

i think the answer is seven, for if i'm being useless °ω°

step-by-step explanation: