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 dropdown with 0.65, 0.77, 0.38, 1.30. applying dropdown, we find that the angle the tent pole makes with the sides of the tent is 39.6 °.

Explanation:

Step1: Calculate the cosine value

The cosine of an angle in a right - triangle is defined as $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, the adjacent side to the angle (the angle the tent pole makes with the sides 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, $\cos\theta=\frac{20}{26}\approx0.77$.

Step2: Find the angle using the inverse cosine function

We know that if $\cos\theta = x$, then $\theta=\cos^{- 1}(x)$. Since $x = \frac{20}{26}\approx0.77$, we apply the inverse cosine function. So, $\theta=\cos^{-1}(0.77)\approx39.6^{\circ}$

Answer:

The ratio is $0.77$ and the operation is the inverse cosine function.