Question

Select the angle that correctly completes the law of cosines for this triangle. 7 2 + 252 – 2(7)(25)cos ___ = 242 A. 180° B. 90° C. 74° D. 16°

Answer 1

74

Explanation:

Answer 2

Option C is correct

The angle A =
`74^(\circ)`

Explanation:

Given:
`7^2+25^2-2(7)(25)\cos\theta = 24^2`

We have to find the angle
`\theta`.

Using Cosine Law:
`b^2+c^2-2ab\cos A = a^2`

Now, simplify:
`7^2+25^2-2(7)(25)\cos\theta = 24^2`

`49+625-350 \cos\theta = 576`

`674-350 \cos\theta = 576` or

`-350 \cos\theta = 576-674`

`-350 \cos\theta = -98`

`\cos \theta = (98)/(350)`

Simplify:

`\cos \theta =0.28`

`\theta = \cos^(-1)(0.28)`

Simplify:

`\theta \approx 74^(\circ)`

Therefore, the angle that completes the law of cosine is: A =
`74^(\circ)`