Question

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

Answer 1

Answer:

$Area \approx 1149\ cm^2$

Step-by-step 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:

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

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 area of given triangle to the nearest square centimetre is:

$Area \approx 1149\ cm^2$