Question

select the correct answer from each drop - down menu.
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 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 trigonometric ratios

In a right - triangle, the cosine of an angle is defined as the ratio of the adjacent side to the hypotenuse. Here, the central pole (adjacent side \(a = 20\) ft) and the slant height (hypotenuse \(c=26\) ft) are given. The cosine of the angle \(\theta\) (the angle the tent pole makes with the sides of the tent) is \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\).

Step2: Calculate the cosine value

\(\cos\theta=\frac{20}{26}\approx0.77\)

Step3: Use the inverse cosine function

If \(\cos\theta = 0.77\), then \(\theta=\cos^{- 1}(0.77)\). Using a calculator, \(\theta\approx39.6^{\circ}\)

Answer:

The first blank: cosine; the second blank: \(0.77\); the third blank: inverse cosine function.