A 75ft tower is located on the side of a hill that is inclin

A 75-ft tower is located on the side of a hill that is inclined 26 degree to the horizontal. A cable is attached to the top of the tower and anchored uphill a distance of 35 ft from the base of the base of the tower. Find the length of the cable. Round to the nearest foot. 67 ft

Solution

Solution:

A 75 ft tower is located on the side of the hill that is inclined 26 degrees to the horizontal.
A cable attached to the top of the tower and anchored uphill a distance of 35 ft from the base of the tower.

The angle opposite the cable is made with the tower and the slanting ground = 90 - 26 = 64 degrees

We can use the law of cosines,

c² = a² + b² - 2ab*cos(C)

where a = 35, b = 75, c = cable length and C = the angle of 64 degrees:

c² = 35² + 75² - 2*35*75*cos(64)
c² = 1225 + 5625 - (5250)*(-0.43837)
c² = 4548.55
c = 67.44 Say c = 67 ft length of cable