Answer:
[tex] Area = 1,309.0 in^2 [/tex]
Step-by-step explanation:
Given:
∆TUV
m < U = 22°
TV = u = 47 in
m < V = 125°
Required:
Area of ∆TUV
Solution:
Find the length of UV using the Law of Sines
[tex] \frac{t}{sin(T)} = \frac{u}{sin(U)} [/tex]
U = 22°
u = TV = 47 in
T = 180 - (125 + 22) = 33°
t = UV = ?
[tex] \frac{t}{sin(33)} = \frac{47}{sin(22)} [/tex]
Multiply both sides by sin(33)
[tex] \frac{t}{sin(33)}*sin(33) = \frac{47}{sin(22)}*sin(33) [/tex]
[tex] t = \frac{47*sin(33)}{sin(22)} [/tex]
[tex] t = 68 in [/tex] (approximated)
[tex] t = UV = 68 in [/tex]
Find the area of ∆TUV
[tex] area = \frac{1}{2}*t*u*sin(V) [/tex]
[tex] = \frac{1}{2}*68*47*sin(125) [/tex]
[tex] = \frac{68*47*sin(125)}{2} [/tex]
[tex] Area = 1,309.0 in^2 [/tex] (to nearest tenth).
