Question

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

Answer 1

`Area \approx 1149\ cm^2`

Explanation:

Given that:

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 = (1)/(2)* a* b* 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 = (1)/(2)* 44* 83* sin141\\\Rightarrow A = (1)/(2) * 3652 * sin141\\\Rightarrow A =1826 * 0.629\\\Rightarrow A \approx 1149\ cm^2`

So, the area of given triangle to the nearest square centimetre is:

`Area \approx 1149\ cm^2`