Answer:
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
