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What is the measurement of the largest angle in ΔABC such that a = 12 cm, b = 26 cm, and c = 19 cm?
25.3°
42.6°
109.4°
112.0°

Sagot :

Mathstudent55idn

Answer:

112.0°

Step-by-step explanation:

In a triangle, the largest angle is opposite the longest side.

The longest side is b, so the largest angle is B.

Since all we have is side lengths, we need to use the law of cosines.

b² = a² + c² - 2ac × cos B

26² = 12² + 19² - 2(12)(19) × cos B

676 = 144 + 361 - 456cos B

-456cosB = 171

cos B = -0.375

B = cos^-1 -0.375

B = 112.0°