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svet-max [94.6K]
3 years ago
10

In ΔUVW, w = 44 cm, u = 83 cm and ∠V=141°. Find the area of ΔUVW, to the nearest square centimeter.

Mathematics
1 answer:
Tema [17]3 years ago
8 0

Answer:

Area  \approx 1149\ cm^2

Step-by-step explanation:

<u>Given that:</u>

ΔUVW,

Side w = 44 cm, (It is the side opposite to \angle W)

Side u = 83 cm (It is the side opposite to \angle U)

and ∠V=141°

Please refer to the attached image with labeling of the triangle with the dimensions given.

Area of a triangle with two sides given and angle between the two sides can be formulated as:

A = \dfrac{1}{2}\times a\times b\times sinC

Where a and b are the two sides and

\angle C is the angle between the sides a and b

Here we have a = w = 44cm

b = u = 44cm

and ∠C= ∠V=141

Putting the values to find the area:

A = \dfrac{1}{2}\times 44\times 83\times sin141\\\Rightarrow A = \dfrac{1}{2} \times 3652 \times sin141\\\Rightarrow A =1826 \times 0.629\\\Rightarrow A  \approx 1149\ cm^2

So, the <em>area </em>of given triangle to the nearest square centimetre is:

Area  \approx 1149\ cm^2

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