Question

Please answer this question now

Answer 1

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

$\frac{UV}{sin(W)} = \frac{VW}{sin(U)}$

W = 34° [180 - (113+33)]

U = 33°

VW = 29 m

UV = ?

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

Multiply both sides by sin(34)

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

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

$UV = 29.8 m$

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)