Question

Please answer this question now

Answer 1

397.7 m²

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

`(UV)/(sin(W)) = (VW)/(sin(U))`

W = 34° [180 - (113+33)]

U = 33°

VW = 29 m

UV = ?

`(UV)/(sin(34)) = (29)/(sin(33))`

Multiply both sides by sin(34)

`(UV*sin(34))/(sin(34)) = (29*sin(34))/(sin(33))`

`UV = (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)