Respuesta :
Answer:
Option C is correct
The angle A = [tex]74^{\circ}[/tex]
Step-by-step explanation:
Given: [tex]7^2+25^2-2(7)(25)\cos\theta = 24^2[/tex]
We have to find the angle [tex]\theta[/tex].
Using Cosine Law: [tex]b^2+c^2-2ab\cos A = a^2[/tex]
Now, simplify: [tex]7^2+25^2-2(7)(25)\cos\theta = 24^2[/tex]
[tex]49+625-350 \cos\theta = 576[/tex]
[tex]674-350 \cos\theta = 576[/tex] or
[tex]-350 \cos\theta = 576-674[/tex]
[tex]-350 \cos\theta = -98[/tex]
[tex]\cos \theta = \frac{98}{350}[/tex]
Simplify:
[tex]\cos \theta =0.28[/tex]
[tex]\theta = \cos^{-1}(0.28)[/tex]
Simplify:
[tex]\theta \approx 74^{\circ}[/tex]
Therefore, the angle that completes the law of cosine is: A =[tex]74^{\circ}[/tex]
