Answer:
397.7 m²
Step-by-step Explanation:
The are of ∆UVW can be found ones we know the measure of 1 angle that is in between known lengths of two sides. Then, we would apply the formula, ½*a*b*sin(θ)
Where, a and b, are the lengths having an included angle (θ), in between them.
To find area of ∆UVW, we need m < V, side lengths of UV and VW.
m < V = 113°
VW = 29 m
UV = ?
Step 1: find UV using the Law of sines
![\frac{UV}{sin(W)} = \frac{VW}{sin(U)}](https://tex.z-dn.net/?f=%20%5Cfrac%7BUV%7D%7Bsin%28W%29%7D%20%3D%20%5Cfrac%7BVW%7D%7Bsin%28U%29%7D%20)
W = 34° [180 - (113+33)]
U = 33°
VW = 29 m
UV = ?
![\frac{UV}{sin(34)} = \frac{29}{sin(33)}](https://tex.z-dn.net/?f=%20%5Cfrac%7BUV%7D%7Bsin%2834%29%7D%20%3D%20%5Cfrac%7B29%7D%7Bsin%2833%29%7D%20)
Multiply both sides by sin(34)
![\frac{UV*sin(34)}{sin(34)} = \frac{29*sin(34)}{sin(33)}](https://tex.z-dn.net/?f=%20%5Cfrac%7BUV%2Asin%2834%29%7D%7Bsin%2834%29%7D%20%3D%20%5Cfrac%7B29%2Asin%2834%29%7D%7Bsin%2833%29%7D%20)
![UV = \frac{29*sin(34)}{sin(33)}](https://tex.z-dn.net/?f=%20UV%20%3D%20%5Cfrac%7B29%2Asin%2834%29%7D%7Bsin%2833%29%7D%20)
![UV = 29.8 m](https://tex.z-dn.net/?f=%20UV%20%3D%2029.8%20m%20)
Step 2: find the area of the triangle
Area = ½*a*b*sin(θ)
a = 29.8 m
b = 29 m
θ = 113°
Area = ½*29.8*29*sin(113)
Area = 397.7 m² (nearest tenth)