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.
A diagram of a cone. The length and height of a cone are 26 feet and 20 feet.
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
.
To find the angle the tent pole makes with the sides of the tent, we can use the tangent function. The tangent of an angle is equal to the opposite side divided by the adjacent side in a right triangle.
In this case, the opposite side is the height of the cone (20 ft) and the adjacent side is the slant height of the tent (26 ft). So the tangent of the angle is:
Tangent of angle = opposite/adjacent = 20/26 = 0.7692
To find the angle, we can take the inverse tangent (or arctan) of 0.7692:
Angle = arctan(0.7692) ≈ 37.61 degrees
Therefore, the angle the tent pole makes with the sides of the tent is approximately 37.61 degrees.