Question

Please answer this question now

Answer 1

Answer:

541.67m²

Step-by-step explanation:

Step 1

We find the third angle

Sum of angles in a triangle = 180°

Third angle = Angle V = 180° - (63 + 50)°

= 180° - 113°

Angle V = 67°

Step 2

Find the sides x and v

We find these sides using the sine rule

Sine rule or Rule of Sines =

a/ sin A = b/ Sin B

Hence for triangle VWX

v/ sin V = w/ sin W = x / sin X

We have the following values

Angle X = 50°

Angle W = 63°

Angle V = 67°

We are given side w = 37m

Finding side v

v/ sin V = w/ sin W

v/ sin 67 = 37/sin 63

Cross Multiply

sin 67 × 37 = v × sin 63

v = sin 67 × 37/sin 63

v = 38.22495m

Finding side x

x / sin X= w/ sin W

x/ sin 50 = 37/sin 63

Cross Multiply

sin 50 × 37 = v × sin 63

x = sin 50 × 37/sin 63

x = 31.81082m

To find the area of triangle VWX

We use heron formula

= √s(s - v) (s - w) (s - x)

Where S = v + w + x/ 2

s = (38.22 + 37 + 31.81)/2

s = 53.515

Area of the triangle = √53.515× (53.515 - 38.22) × (53.515 - 37 ) × (53.515 - 31.81)

Area of the triangle = √293402.209

Area of the triangle = 541.66614164081m²

Approximately to the nearest tenth = 541.67m²