Answer:
[tex] Area = 112.1 m^2 [/tex]
Step-by-step 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
[tex] \frac{w}{sin(W)} = \frac{x}{sin(X)} [/tex]
X = 130°
x = WY = 31 mm
W = 180 - (130 + 26) = 24°
w = XY = ?
[tex] \frac{w}{sin(24)} = \frac{31}{sin(130)} [/tex]
Multiply both sides by sin(24) to solve for x
[tex] \frac{w}{sin(24)}*sin(24) = \frac{31}{sin(130)}*sin(24) [/tex]
[tex] w = \frac{31*sin(24)}{sin(130)} [/tex]
[tex] w = 16.5 mm [/tex] (approximated)
[tex] XY = w = 16.5 mm [/tex]
Find the area of ∆WXY
[tex] area = \frac{1}{2}*w*x*sin(Y) [/tex]
[tex] = \frac{1}{2}*16.5*31*sin(26) [/tex]
[tex] = \frac{16.5*31*sin(26)}{2} [/tex]
[tex] Area = 112.1 m^2 [/tex] (to nearest tenth).
