A 10 ft . tent pole has a support rope that extends from the top of the pole to the ground. The rope and the ground form a \( 30^{\circ} \) angle. How long is the rope, rounded to the tenth place? (1 point) (0 20.0 ft . (17.3 ft . (11.5 ft .

To find the length of the rope, we can use the sine function, which relates the angle to the opposite side (the height of the pole) and the hypotenuse (the rope). Here, the height of the tent pole is 10 ft, and we know the angle is \( 30^{\circ} \). Using the sine relation: \[ \sin(30^{\circ}) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{10}{\text{rope length}} \] Since \( \sin(30^{\circ}) = 0.5 \): \[ 0.5 = \frac{10}{\text{rope length}} \Rightarrow \text{rope length} = \frac{10}{0.5} = 20 \text{ ft}. \] So the rope length is 20.0 ft. If we were solving this problem without a calculator, remember to keep orientation in mind! Labeling your diagrams can prevent common mistakes, such as mixing up adjacent and opposite sides or confusing angles. Diagrams also make it easier to visualize relationships and calculations!