Question

Please answer this question now

Answer 1

Answer:

$Area = 538.5 m^2$

Step-by-step Explanation:

Given:

∆XVW

m < X = 50°

m < W = 63°

XV = w = 37 m

Required:

Area of ∆XVW

Solution:

Find side length XW using Law of Sines

$\frac{v}{sin(V)} = \frac{w}{sin(W)}$

W = 63°

w = XV = 37 m

V = 180 - (50+63) = 67°

v = XW = ?

$\frac{v}{sin(67)} = \frac{37}{sin(63)}$

Cross multiply

$v*sin(63) = 37*sin(67)$

Divide both sides by sin(63) to make v the subject of formula

$\frac{v*sin(63)}{sin(63)} = \frac{37*sin(67)}{sin(63)}$

$v = \frac{37*sin(67)}{sin(63)}$

$v = 38$ (approximated to nearest whole number)

$XW = v = 38 m$

Find the area of ∆XVW

$area = \frac{1}{2}*v*w*sin(X)$

$= \frac{1}{2}*38*37*sin(50)$

$= \frac{38*37*sin(50)}{2}$

$Area = 538.5 m^2$ (to nearest tenth).