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469.4ft² of 469.4 square feet

Step-by-step explanation:

In the above question, we are given ∆ WXY

In the question, we have the following values already:

Angle W = 27°

Angle X = unknown

Angle Y = 40°

Side w = unknown

Side x = unknown

Side y = 38ft

Area of the triangle= it is unknown as well

First Step

We would determine the third angle = Angle X

Sum of angles in a triangle = 180°

= Angle X= 180° - (27 + 40)°

= 180° - 67°

Angle X = 113°

Second step

Determine the sides w and x

We find these sides using the sine rule

Sine rule =

a/ sin A = b/ Sin B

Hence for triangle WXY

w/ sin W = x/ sin X = y/ sin Y

a) side w

w/ sin W= y/ sin Y

w/sin 27 = 38/sin 40

Cross Multiply

sin 27 × 38 = w × sin 40

w = sin 27 × 38/sin 40

w = 26.83879ft

w = 26.84ft

Finding side x

x / sin X= y/ sin Y

x/ sin 113 = 38/sin 40

Cross Multiply

sin 113 × 38 = x × sin 40

x = sin 113 × 38/sin 40

x = 54.41795ft

x = 54.42ft

To find the area of triangle WXY

We use heron formula, which is given as:

= √s(s - w) (s - x) (s - y)

Where S = w + x + y/ 2

s = (38 + 26.84 + 54.42)/2

s = 59.63

Area of the triangle

= √59.63× (59.63 - 38) × (59.63 - 26.84 ) × (59.63 - 54.42)

Area of the triangle = √220343.61423

Area of the triangle = 469.40772706541ft²

Therefore, approximately to the nearest tenth , the Area of ∆WXY =469.4yd²

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