Question

Please answer now correct answer fast

Answer 1

Answer:

$Area = 112.1 m^2$

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

$\frac{w}{sin(W)} = \frac{x}{sin(X)}$

X = 130°

x = WY = 31 mm

W = 180 - (130 + 26) = 24°

w = XY = ?

$\frac{w}{sin(24)} = \frac{31}{sin(130)}$

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

$\frac{w}{sin(24)}*sin(24) = \frac{31}{sin(130)}*sin(24)$

$w = \frac{31*sin(24)}{sin(130)}$

$w = 16.5 mm$ (approximated)

$XY = w = 16.5 mm$

Find the area of ∆WXY

$area = \frac{1}{2}*w*x*sin(Y)$

$= \frac{1}{2}*16.5*31*sin(26)$

$= \frac{16.5*31*sin(26)}{2}$

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