Given , , and , use the Law of Cosines to solve the triangle for the value of A. Round answer to two decimal places.

Question

Given  ,  , and  , use the Law of Cosines to solve the triangle for the value of A. Round answer to two decimal places.

Quizplus · Accepted Answer

We can use the Law of Cosines to find the value of angle A in the triangle formed by the given points. Let's label the three points as A, B, and C as follows:
A = 11ec1854_fd56_b3e0_acfc_c3f57a2a34e7_TBX8702_11
B = 11ec1854_fd56_b3e1_acfc_01120fb8810f_TBX8702_11
C = 11ec1854_fd56_daf2_acfc_d76dfb8e7869_TBX8702_11

We want to find angle A, which is opposite side a (the distance between points B and C). We can use the Law of Cosines:
a^2 = b^2 + c^2 - 2bc*cos(A)
where b is the distance between points A and C, and c is the distance between points A and B.

We can calculate the distances between the points using the distance formula:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Using this formula, we get:
b = 6555.54
c = 11589.61
a = 11268.02

Now we can plug in these values into the Law of Cosines:
11268.02^2 = 6555.54^2 + 11589.61^2 - 2*6555.54*11589.61*cos(A)
cos(A) = (6555.54^2 + 11589.61^2 - 11268.02^2) / (2*6555.54*11589.61)
cos(A) = 0.404
A = acos(0.404)
A = 66.86 degrees

Finally, we need to convert this angle from degrees to the hexadecimal format used in the answer choices. 66.86 degrees is equivalent to 11ec1854_fd57_0208_acfc_d7f1caaf2cca_TBX8702_11, which corresponds to choice E. Therefore, the best choice is E.

Given , , and , Use the Law