Question

Please answer this question now

Answer 1

Answer:

$Area = 400.4 m^2$

Step-by-step Explanation:

Given:

∆UVW,

m < U = 33°

m < V = 113°

VW = u = 29 m

Required:

Area of ∆UVW

Solution:

Find side length UV using Law of Sines

$\frac{u}{sin(U)} = \frac{w}{sin(W)}$

U = 33°

u = VW = 29 m

W = 180 - (33+113) = 34°

w = UV = ?

$\frac{29}{sin(33)} = \frac{w}{sin(34)}$

Cross multiply

$29*sin(34) = w*sin(33)$

Divide both sides by sin(33) to make w the subject of formula

$\frac{29*sin(34)}{sin(33)} = \frac{w*sin(33)}{sin(33)}$

$\frac{29*sin(34)}{sin(33)} = w$

$29.77 = w$

$UV = w = 30 m$ (rounded to nearest whole number)

Find the area of ∆UVW using the formula,

$area = \frac{1}{2}*u*w*sin(V)$

$= \frac{1}{2}*29*30*sin(113)$

$= \frac{29*30*sin(113)}{2}$

$Area = 400.4 m^2$ (to nearest tenth).