Question

A player on the show Survivor is constructing a triangular hut. He uses a 13 foot branch of bamboo for one side and an 11 foot branch of bamboo for the other. When he secures the 11 foot branch to the ground, it forms a 72 degree angle. What angle would the 13 foot bamboo make with the ground?

Answer 1

The angle that the 13 foot bamboo makes with the ground is approximately 79.24 degrees.

To find the angle that the 13 foot bamboo makes with the ground, we can use the properties of a triangle. Since we know the length of two sides and one angle, we can use the law of cosines to find the missing angle.

Using the law of cosines, we have:

c^2 = a^2 + b^2 - 2ab * cos(C)

where c is the length of the unknown side (13 feet), a and b are the lengths of the known sides (11 feet and 13 feet), and C is the unknown angle.

Plugging in the values, we get:

169 = 121 + 169 - 2 * 11 * 13 * cos(C)

Simplifying, we have:

48 = 286 * cos(C)

cos(C) = 48 / 286

Using a calculator, we find that the value of cos(C) is approximately 0.1674. Taking the inverse cosine, we find that the angle C is approximately 79.24 degrees.