The measure of angle A rounded to the nearest whole number is 25°.
Hence, option C is the correct answer.
What is the measure of angle A?
Given that?
- side a = 20cm
- side b = 13cm
- Angle C = 139°
- side c = ?
- Angle A = ?
First, we determine the length of side c using the law of cosines.
c = √( a² + b² - 2ab( cosC ) )
We substitute in our values
c = √( 20² + 13² - 2×20×13( cos 139° ) )
c = √( 400 + 169 - 520( cos 139° ) )
c = √( 569 + 392.44898 )
c = √961.44898
c = 31 cm
Next, we find Angle A, using the law of cosines.
A = cos⁻¹[ ( b² + c² - a² ) / 2cb ]
We substitute in our values
A = cos⁻¹[ ( 13² + 31² - 20² ) / ( 2 × 31 × 13 ) ]
A = cos⁻¹[ ( 169 + 961 - 400) / 806]
A = cos⁻¹[ 730 / 806]
A = cos⁻¹[ 0.9057 ]
A = 25°
The measure of angle A rounded to the nearest whole number is 25°.
Hence, option C is the correct answer.
Learn more about law of cosines here: https://brainly.com/question/17289163
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