Solve for x. Round to the nearest tenth.
5,14 side of triangle
X degree. Degrees of angle
Answers
A. 18
B. 21
C. 22
To solve for x, we will use the Law of Sines, which states that in a triangle, the ratio of the length of a side to the sine of its opposite angle is equal for all sides and their corresponding angles.
In this case, the side 5 corresponds to the angle x, and the side 14 corresponds to the angle x's opposite angle. So, we can set up the following equation:
sin(x)/5 = sin(180° - x)/14
To solve for x, we can cross-multiply and simplify:
14sin(x) = 5sin(180° - x)
Using the identity sin(180° - x) = sin(x), the equation becomes:
14sin(x) = 5sin(x)
Dividing both sides by sin(x), we get:
14 = 5
This is not possible, so we made an error in setting up the original equation. We will try again using the Law of Cosines.
The Law of Cosines states that in a triangle, the square of one side is equal to the sum of the squares of the other two sides minus twice the product of the lengths of those sides multiplied by the cosine of their included angle.
For this triangle with sides 5 and 14:
14^2 = 5^2 + x^2 - 2(5)(x)cos(x)
Simplifying:
196 = 25 + x^2 - 10xcos(x)
Rearranging:
0 = x^2 - 10xcos(x) - 171
Since we are looking for a degree measure for x, we can use trial and error or a calculator to find the value of x that satisfies the equation. Trying the answer choices:
A. 18:
0 = 18^2 - 10(18)cos(18) - 171
This equation does not equal zero.
B. 21:
0 = 21^2 - 10(21)cos(21) - 171
This equation does not equal zero.
C. 22:
0 = 22^2 - 10(22)cos(22) - 171
This equation does not equal zero.
None of the answer choices satisfy the equation, so we cannot find a value for x that satisfies the conditions given.