For the triangle shown <B= 34 degrees and CD= 80
If we know that angle B = 34 degrees and CD = 80, we can solve for the other missing parts of the triangle using trigonometry.
First, we can use the sine law to find angle C, since we know that angle A = 180 - 34 - C. Using the sine law:
sin(34) / CD = sin(C) / AC
sin(34) / 80 = sin(C) / AC
sin(C) = (80 * sin(34)) / AC
C = sin^(-1)((80 * sin(34)) / AC)
Now, we can use the cosine law to find the length of side AC:
AC^2 = 80^2 + CD^2 - 2 * 80 * CD * cos(34)
AC^2 = 80^2 + 80^2 - 2 * 80 * 80 * cos(34)
AC^2 = 6400 + 6400 - 12800 * cos(34)
AC = sqrt(12800 - 12800 * cos(34))
Now that we have found the lengths of all sides and angles of the triangle, we can calculate any other missing information or solve for any other particular problem that may arise.