Answer:
Area = 19.9 mm²
Step-by-step explanation:
Step 1: Find Angle V.
m < V = 180 - (131 + 27) (sum of angles in a triangle)
V = 22°
Step 2: Find UW using the law of sines.
[tex] \frac{UW}{sin(V)} = \frac{UV}{sin(W)} [/tex]
Plug in your values
[tex] \frac{UW}{sin(22)} = \frac{8}{sin(27)} [/tex]
Multiply both sides by sin(22) to solve for UW
[tex] \frac{UW*sin(22)}{sin(22)} = \frac{8*sin(22)}{sin(27)} [/tex]
[tex] UW = \frac{8*sin(22)}{sin(27)} [/tex]
[tex] UW = 6.6 mm [/tex]
Step 3: Find the area of ∆UVW
Area = ½*UW*UV*Sin(U)
Area = ½*6.6*8*sin(131)
Area = 3.3*8*sin(131)
Area = 19.9 mm² (to the nearest tenth)
