Based on the calculations, the area of this triangle is equal to 290,136.87 m².
Given the following data:
Mathematically, the area of a triangle can be calculated by using this formula:
Area = 1/2 × b × h
Where:
In this scenario, the area of this triangle is given by:
Area = 1/2 × a × b × sinC
Substituting the given parameters into the formula, we have:
Area = 1/2 × 757.64 × 946.70 × sin(54°18'25")
Area = 580,273.74/2
Area = 290,136.87 m².
Next, we would determine the probable error of the area by using this formula:
[tex]PE_A = \pm k \sqrt{PE} \\\\PE_A = \pm \frac{1}{2} \times sinC \sqrt{(aPE_b)^2 + (bPE_a)^2 } \\\\PE_A = \pm \frac{1}{2} \times sin(54^{\circ}18'25") \times \sqrt{(757.64 \times 0.045)^2 + (946.70 \times 0.055)^2 } \\\\PE_A = \pm 0.4045 \times \sqrt{1,162.39 +2,711.12}\\\\PE_A = \pm 0.4045 \times \sqrt{3,873.51}\\\\PE_A = \pm 0.4045 \times 62.2375\\\\PE_A = \pm25.1751 \;m^2[/tex]
Therefore, probable error of the area is equal to ±25.1751 m².
Read more on area of triangle here: brainly.com/question/21917592
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Complete Question:
Two sides and the included angle of a triangle were measured and the probable error of each value were computed as follows:
A = 757.64 +0.045 m
B = 946.70+ 0.055 m
C = 54°18'25"
Determine the area of the triangle and the probable error of the area.
