Question

Please answer this question now

Answer 1

`Area = 538.5 m^2`

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

`(v)/(sin(V)) = (w)/(sin(W))`

W = 63°

w = XV = 37 m

V = 180 - (50+63) = 67°

v = XW = ?

`(v)/(sin(67)) = (37)/(sin(63))`

Cross multiply

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

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

`(v*sin(63))/(sin(63)) = (37*sin(67))/(sin(63))`

`v = (37*sin(67))/(sin(63))`

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

`XW = v = 38 m`

Find the area of ∆XVW

`area = (1)/(2)*v*w*sin(X)`

`= (1)/(2)*38*37*sin(50)`

`= (38*37*sin(50))/(2)`

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