Question

in the triangle below, which equation can be used to solve for x (side UW)?

triangle VUW
angle V=75 degrees
angle U= 50 degrees
side VU= 13 ft

solve for side UW

x=13sin50/sin75
x=13sin75/sin50
x=13sin55/sin55
x=13sin75/sin55

Answer 1

Answer:

The value of x is

$\frac{13\:sin\:75}{sin\:55}$

Step-by-step explanation:

Formula used:

Sine formula:

In triangle ABC,

$\frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC}$

Here, a, b and c are sides opposite to angles A, B and C

Given:

∠U = 50°

∠V = 75°

∠W = 55° ( since sum of the angles of a riangle is 180°)

In triangle UVW,

By sine formula,

$\frac{VW}{sinU}=\frac{x}{sinV}=\frac{13}{sinW}$

$\frac{VW}{sin\:50}=\frac{x}{sin\:75}=\frac{13}{sin\:55}$

$\frac{x}{sin\:75}=\frac{13}{sin\:55}$

$x=\frac{13\:sin\:75}{sin\:55}$

Answer 2

Answer:

X = 13Sin75°/Sin55°  is the right answer

Step-by-step explanation:

triangle VUW  

angle V=75 degrees

angle U= 50 degrees

side VU= 13 ft

∠V + ∠U +∠W = 180°

=> 75° + 50° + ∠W = 180°

=> ∠W = 55°

VU/Sin∠W = UW/Sin∠V  = VW/Sin∠U

=> 13/Sin55° = UW/Sin75°

=> UW = 13Sin75°/Sin55°

=> X = 13Sin75°/Sin55°  is the right answer