Question

What the correct answer now

Answer 1

`Area = 1,309.0 in^2`

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

`(t)/(sin(T)) = (u)/(sin(U))`

U = 22°

u = TV = 47 in

T = 180 - (125 + 22) = 33°

t = UV = ?

`(t)/(sin(33)) = (47)/(sin(22))`

Multiply both sides by sin(33)

`(t)/(sin(33))*sin(33) = (47)/(sin(22))*sin(33)`

`t = (47*sin(33))/(sin(22))`

`t = 68 in` (approximated)

`t = UV = 68 in`

Find the area of ∆TUV

`area = (1)/(2)*t*u*sin(V)`

`= (1)/(2)*68*47*sin(125)`

`= (68*47*sin(125))/(2)`

`Area = 1,309.0 in^2` (to nearest tenth).