Please answer this in two minutes

469.4ft²

Step-by-step explanation:

We have ∆ WXY in the above question,

From which we have obtained the following values

Angle W = 27°

Angle X = ?

Angle Y = 40°

Side w =?

Side x = ?

Side y = 38ft

Area of the triangle= ?

Step 1

We find Angle X

We know that the Sum of angles in a triangle = 180°

In the question above, we are given 2 angles

Hence,

Angle X = 180 - ( Angle W + Angle Y)

= 180° - (27 + 40)°

= 180° - 67°

Angle X = 113°

Step 2

Find the sides w and x

We find these sides using the Rule of sines

Rule of Sines =

a/ sin A = b/ Sin B = c/Sin C

Hence for triangle WXY

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

We have the following values

Angle W = 27°

Angle X = 113°

Angle Y = 40°

We are given side y = 38ft

Determining 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

Determining side x

w/ sin W = x/ sin X

26.84/ sin 27 = x/sin 113

Cross Multiply

sin 113 × 26.84 = x × sin 27

x = sin 113 × 26.84/sin 27

x = 54.42041ft

x = 54.42ft

To find the area of triangle WXY

We apply the use of heron formula

= √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

Hence, Approximately to the nearest tenth =469.4yd²