Question

a 10 - foot pole is supporting a tent and has a rope attached to the top. the rope is pulled straight and the other end is attached to a peg one foot above the ground. the rope and the pole form an angle that measures 35°, as shown below. which expression shows the length of the rope? $\frac{9}{cos35^{circ}}approx11.0$ feet $\frac{9}{cos35^{circ}} + 1approx12.0$ feet $\frac{10}{cos35^{circ}}-1approx11.2$ feet $\frac{10}{cos35^{circ}}approx12.2$ feet

Explanation:

Step1: Determine vertical distance

The vertical distance from the top of the pole to the peg - attachment point is \(10 - 1=9\) feet.

Step2: Use cosine function

In a right - triangle formed by the pole, the ground, and the rope, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, \(\theta = 35^{\circ}\), the adjacent side to the \(35^{\circ}\) angle is the vertical distance of 9 feet, and the hypotenuse is the length of the rope \(L\). So, \(\cos35^{\circ}=\frac{9}{L}\), and we can solve for \(L\) as \(L=\frac{9}{\cos35^{\circ}}\).

Answer:

\(\frac{9}{\cos35^{\circ}}\approx11.0\) feet