Please show work for 8, 9 & 10. Please do all , not just one. Use the Law of Cos

Question

Please show work for 8, 9 & 10. Please do all, not just one.

Use the Law of Cosines to solve the triangle. Round your answers to two decimal places. A = 45 degree, b = 4, c = 10 Complete the table by solving the parallelogram shown in the figure. (The lengths of the diagonals are given by c and d.) A 110-foot vertical tower is to be erected on the side of a hill that makes a angle with the horizontal (see figure). Find the length of each of the two guy wires that will be anchored 75 feet uphill and downhill from the base of the tower.

Explanation / Answer

A = 45 , b = 4 and c = 10

We have
a^2 = b^2 + c^2 - 2bccos(A)

a^2 = 16 + 100 - 2(4)(10)cos(45)

a^2 = 59.43145750504

a = 7.71

a/sinA = b/sinB

7.71/sin(45) = 4/sin(B)

B = 21.52 degrees

Now,
c/sinC = a/sinA

10/sinC = 7.71/sin(45)

C = 66.51 degrees

So, answers :
a = 7.71
B = 21.52
C = 66.51

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