Question

Trigonometry, Law of Cosines.

Select the angle that correctly completes the law of cosines for this triangle.

Answer 1

○ C.
`\displaystyle 74°`

Explanation:

`\displaystyle c^2 + b^2 - 2cb\:cos∠A = a^2`

In the EDGE formula of the Law of Cosines, whatever squared edge term is on the outside of the equivalence symbol, its angle measure is what you write next to the trigonometric function, if you understand the formula written above.

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Answer 2

The Law of Cosines, applied to a triangle with sides 24, 7, and 25, reveals that the missing angle A is approximately 74°. Here option C is correct.

The Law of Cosines states that for any triangle with sides a, b, and c and opposite angles A, B, and C, the following equation holds:

a^2 = b^2 + c^2 - 2bc cos A

In this case, a = 24, b = 7, c = 25, and A is the unknown angle. Plugging in the values, we get:

24^2 = 7^2 + 25^2 - 2(7)(25) cos A

Solving for cos A, we get:

cos A = (7^2 + 25^2 - 24^2) / (2(7)(25)) = 0.276

Taking the inverse cosine of both sides, we get:

A = cos^-1 (0.276) = 74° (rounded to the nearest degree)

Therefore, the angle that correctly completes the Law of Cosines for this triangle is 74°. Here option C is correct.