Question

a conical circus tent has a 20 ft central pole that supports it. the slant height of the tent is 26 ft long. explain how to find the angle the tent pole makes with the sides of the tent.
the central pole forms a right triangle with the floor of the tent. the cosine of the missing angle is the ratio of the length of the central pole to the length of the side of the tent, which is. applying, we find that the angle the tent pole makes with the sides of the tent is 39.6 °.

Explanation:

Step1: Recall cosine definition

In a right - triangle, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, the adjacent side to the angle (between the central pole and the side of the tent) is the length of the central pole ($a = 20$ ft), and the hypotenuse is the slant height of the tent ($c=26$ ft). So, $\cos\theta=\frac{20}{26}=\frac{10}{13}\approx0.7692$.

Step2: Use inverse cosine

To find the angle $\theta$, we use the inverse cosine function. If $\cos\theta = x$, then $\theta=\cos^{-1}(x)$. So, $\theta=\cos^{-1}(\frac{10}{13})$. Using a calculator, $\cos^{-1}(0.7692)\approx39.6^{\circ}$.

Answer:

The ratio is $\frac{20}{26}$ (or $\frac{10}{13}$), and the operation is the inverse cosine ($\cos^{-1}$).