Thanks The figure shows a 800 fort tower on the side of a hi

The figure shows a 800 fort tower on the side of a hill that forms a 8 degree angle with the horizontal. Find the length of each of the two guy wires that are anchored 70 feet uphill and downhill from the tower\'s base and extend to the top of the tower. Part (a) What is the length of the uphill guy wire?

Solution

Let:
AB be horizontal ground,
AC be the hill,
D be the foot of the tower,
E be the top of the tower.

Extend ED to meet AB at F.
Angle AFE = 90 deg.
Angle FAD = 8 deg.

Therefore:
Angle ADF = 82 deg.
Angle EDS = 82 deg.
Angle ADE = 98 deg.

In triangle AED, you now know ED = 800 ft, AD = 70 ft, and angle ADE = 98 deg.

Using the cosine rule:
AE^2 = 70^2 + 800^2 - 2 * 70 * 800 cos(98)
AE = 812.7 ft.

Similarly for triangle EDC:
EC^2 = 70^2 + 800^2 - 2 * 70 * 800 cos(82)
EC = 793.3 ft.