At Westonci.ca, we connect you with experts who provide detailed answers to your most pressing questions. Start exploring now! Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.
Sagot :
Certainly! Let's solve for the angle [tex]\( C \)[/tex] using the Law of Cosines:
The Law of Cosines states:
[tex]\[ c^2 = a^2 + b^2 - 2ab \cdot \cos C \][/tex]
We need to solve for [tex]\( C \)[/tex]. First, we can rearrange the formula to isolate [tex]\( \cos C \)[/tex]:
[tex]\[ \cos C = \frac{a^2 + b^2 - c^2}{2ab} \][/tex]
Now, let's plug in the given values [tex]\( a = 7 \)[/tex], [tex]\( b = 10 \)[/tex], and [tex]\( c = 5 \)[/tex]:
[tex]\[ \cos C = \frac{7^2 + 10^2 - 5^2}{2 \cdot 7 \cdot 10} \][/tex]
Calculating the squares and the product in the denominator:
[tex]\[ \cos C = \frac{49 + 100 - 25}{140} \][/tex]
[tex]\[ \cos C = \frac{124}{140} \][/tex]
[tex]\[ \cos C = 0.8857142857142857 \][/tex]
Next, we need to find [tex]\( C \)[/tex] by taking the arccosine (inverse cosine) of the calculated value:
[tex]\[ C = \arccos(0.8857142857142857) \][/tex]
This gives us [tex]\( C \)[/tex] in radians:
[tex]\[ C \approx 0.48276592332573415 \text{ radians} \][/tex]
To convert radians to degrees:
[tex]\[ C_{\text{degrees}} = C \times \frac{180}{\pi} \][/tex]
Substituting the value we have:
[tex]\[ C_{\text{degrees}} \approx 0.48276592332573415 \times 57.2958 \][/tex]
[tex]\[ C_{\text{degrees}} \approx 27.660449899300872 \][/tex]
Therefore, the cosine of angle [tex]\( C \)[/tex] is approximately [tex]\( 0.8857142857142857 \)[/tex], the angle [tex]\( C \)[/tex] in radians is approximately [tex]\( 0.48276592332573415 \)[/tex] radians, and the angle [tex]\( C \)[/tex] in degrees is approximately [tex]\( 27.66^\circ \)[/tex].
The Law of Cosines states:
[tex]\[ c^2 = a^2 + b^2 - 2ab \cdot \cos C \][/tex]
We need to solve for [tex]\( C \)[/tex]. First, we can rearrange the formula to isolate [tex]\( \cos C \)[/tex]:
[tex]\[ \cos C = \frac{a^2 + b^2 - c^2}{2ab} \][/tex]
Now, let's plug in the given values [tex]\( a = 7 \)[/tex], [tex]\( b = 10 \)[/tex], and [tex]\( c = 5 \)[/tex]:
[tex]\[ \cos C = \frac{7^2 + 10^2 - 5^2}{2 \cdot 7 \cdot 10} \][/tex]
Calculating the squares and the product in the denominator:
[tex]\[ \cos C = \frac{49 + 100 - 25}{140} \][/tex]
[tex]\[ \cos C = \frac{124}{140} \][/tex]
[tex]\[ \cos C = 0.8857142857142857 \][/tex]
Next, we need to find [tex]\( C \)[/tex] by taking the arccosine (inverse cosine) of the calculated value:
[tex]\[ C = \arccos(0.8857142857142857) \][/tex]
This gives us [tex]\( C \)[/tex] in radians:
[tex]\[ C \approx 0.48276592332573415 \text{ radians} \][/tex]
To convert radians to degrees:
[tex]\[ C_{\text{degrees}} = C \times \frac{180}{\pi} \][/tex]
Substituting the value we have:
[tex]\[ C_{\text{degrees}} \approx 0.48276592332573415 \times 57.2958 \][/tex]
[tex]\[ C_{\text{degrees}} \approx 27.660449899300872 \][/tex]
Therefore, the cosine of angle [tex]\( C \)[/tex] is approximately [tex]\( 0.8857142857142857 \)[/tex], the angle [tex]\( C \)[/tex] in radians is approximately [tex]\( 0.48276592332573415 \)[/tex] radians, and the angle [tex]\( C \)[/tex] in degrees is approximately [tex]\( 27.66^\circ \)[/tex].
We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.