Question

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°

Answer 1

The largest angle in triangle ABC is approximately 42.6°.

Step-by-step explanation:

In triangle ABC, we can use the Law of Cosines to find the largest angle. The Law of Cosines states that in a triangle with sides a, b, and c and opposite angles A, B, and C, the following equation holds:

c^2 = a^2 + b^2 - 2ab * cos(C)

Given that a = 12 cm, b = 26 cm, and c = 19 cm, we can substitute these values into the equation:

19^2 = 12^2 + 26^2 - 2(12)(26) * cos(C)

Simplifying the equation gives:

361 = 144 + 676 - 624 * cos(C)

Now, we can solve for cos(C):

624 * cos(C) = 821 - 361

cos(C) = 460/624 = 0.7371795

To find the measure of angle C, we can use the inverse cosine function:

C = cos^{-1}(0.7371795)

Using a calculator, we find that C ≈ 42.6°

Answer 2

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°