Question

A guy wire 1393 feet long is attached to the top of a tower. When pulled taut, it touches level ground 741 feet from the base of the tower. What angle does the wire make with the ground? Express your answer using degree measure rounded to one decimal place.

Answer 1

Answer:

  57.9°

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the relation between trig functions and sides of a right triangle. Here, you're given the side adjacent to the angle of interest, and the hypotenuse of the triangle. This suggests the CAH relationship is the one of interest:

  Cos = Adjacent/Hypotenuse

  cos(angle) = (741 ft)/(1393 ft)

  angle = arccos(741/1393) ≈ 57.863° . . . . . use the inverse cosine function

  angle ≈ 57.9°

The wire makes an angle of approximately 57.9° with the ground.