Question

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Answer 1

`Area = 112.1 m^2`

Explanation:

Given:

∆WXY

m < X = 130°

WY = x = 31 mm

m < Y = 26°

Required:

Area of ∆WXY

Solution:

Find the length of XY using Law of Sines

`(w)/(sin(W)) = (x)/(sin(X))`

X = 130°

x = WY = 31 mm

W = 180 - (130 + 26) = 24°

w = XY = ?

`(w)/(sin(24)) = (31)/(sin(130))`

Multiply both sides by sin(24) to solve for x

`(w)/(sin(24))*sin(24) = (31)/(sin(130))*sin(24)`

`w = (31*sin(24))/(sin(130))`

`w = 16.5 mm` (approximated)

`XY = w = 16.5 mm`

Find the area of ∆WXY

`area = (1)/(2)*w*x*sin(Y)`

`= (1)/(2)*16.5*31*sin(26)`

`= (16.5*31*sin(26))/(2)`

`Area = 112.1 m^2` (to nearest tenth).