Answer:
In this problem, we have a right triangle where the hypotenuse is the 30-foot support cable and one leg is 22 feet (the distance from the base of the pole to where the cable is attached). To find the angle that the cable makes with the ground, we need to use trigonometry. The tangent of an angle in a right triangle is equal to the length of the opposite side divided by the length of the adjacent side. In this case, we want to find tan(θ), where θ is the angle between the cable and the ground. Therefore, tan(θ) = opposite/adjacent = 22/30 = 0.7333. Taking inverse tangent on both sides gives us θ = tan^-1(0.7333) ≈ 36.7 degrees to one decimal place. Therefore, to the nearest tenth, the measure of the angle that the cable makes with the ground is approximately 36.7 degrees.