A guy wire to a tower makes a 71° angle with level ground. At a point 36 ft farther from the tower than the wire but on the same side as the base of the wire, the angle of elevation to the top of the tower is 36°. Find the length of the wire (to the nearest foot). *

The length of the wire is 37.15 ft

Explanation:

The figure is attached for the reference.

tan (71) =

tan (36) =

So,

tan(36) (36 + x) = y

tan(71) =

Substituting x = 12.11 ft in equation 1:

Length of the wire, z =

So,

Therefore, the length of the wire is 37.15 ft

let soccer = x and golf = y

part a

1st equation: x + y = 125

2nd equation: x = y +45

part b

replace x in the 1st equation with the 2nd one:

y + 45 + y = 125

simplify:

2y + 45 = 125

subtract 45 from each side:

2y = 80

divide both sides by 2:

y = 80/2

y = 40

she plays golf for 40 minutes.

part c

no because she plays soccer for 45 minutes longer than golf 40 +45 =   85 minutes, not 80 minutes.