Answer:
35.6 yd²
Step-by-step explanation:
Area of ∆UVW can be solved if we know the lengths of 2 sides and their included angle.
We are Given just 1 side, UV (w). Use the law of sines to find UW (v).
Thus:
[tex] \frac{v}{sin(V)} = \frac{w}{sin(W)} [/tex]
W = 137°
w = 19 yd
V = 180 - (137 + 22) = 21° => sum of triangle
v = ??
Plug in the values and solve for v
[tex] \frac{v}{sin(21)} = \frac{19}{sin(137)} [/tex]
Multiply both sides by sin(21)
[tex] \frac{v}{sin(21)}*sin(21) = \frac{19}{sin(137)}*sin(21) [/tex]
[tex] v = \frac{19*sin(21)}{sin(137)} [/tex]
[tex] v = 10 yd [/tex] (approximated)
Find area of ∆UVW:
Area = ½*UV*UW*sin(U)
Area = ½*v*w*sin(U)
= ½*10*19*sin(22)
Area = 35.6 yd² (to nearest tenth)
