Find the measure of side c.
8.8
10.3
9.7
8.5
The Correct Answer and Explanation is :
To find the measure of side ( c ) in a triangle where the other sides are given, we can use the Law of Cosines, which states:
[
c^2 = a^2 + b^2 – 2ab \cdot \cos(C)
]
where:
- ( c ) is the side opposite angle ( C ),
- ( a ) and ( b ) are the other two sides,
- ( C ) is the angle opposite side ( c ).
Assuming you have the lengths of sides ( a ) and ( b ) (e.g., 8.8 and 10.3) and the angle ( C ) (not specified in your question), you can plug in the values.
Let’s assume:
- ( a = 8.8 )
- ( b = 10.3 )
- ( C = 9.7^\circ ) (this is a hypothetical value for illustration).
- Calculate ( a^2 ) and ( b^2 ):
[
a^2 = 8.8^2 = 77.44
]
[
b^2 = 10.3^2 = 106.09
] - Calculate ( 2ab \cdot \cos(C) ):
[
\cos(9.7^\circ) \approx 0.9848 \quad \text{(using a calculator)}
]
[
2ab \cdot \cos(C) = 2 \cdot 8.8 \cdot 10.3 \cdot 0.9848 \approx 181.56
] - Substituting into the Law of Cosines:
[
c^2 = 77.44 + 106.09 – 181.56
]
[
c^2 \approx 1.97
]
[
c \approx \sqrt{1.97} \approx 1.4
]
Thus, the measure of side ( c ) is approximately 1.4 units.
If you can provide the specific angle or clarify the question further, I can refine this calculation accordingly!