You're concerned that your neighbor's backyard flagpole may fall over in heavy winds (it looked really wobbly during the last thunderstorm), and you're hoping it doesn't fall over and hit your house. one afternoon, you notice that the four-foot high chain-link fence is casting a shadow seven feet long, while the neighbor's pole is casting a shadow 26 feet long. the base of the pole is 18 feet from your house. is your house safe?

Yes you can have some peace of mind, because your house is safe. Since, the flagpole is only 14.85 feet, is shorter than the 18 feet of distance from its base to your home.

Step-by-step explanation:

What you need to do is to estimate the height of the pole using its shadow, and the relationship between the height of the fence and it respective shadow:

For a rectangle triangle, the proportion of its shorter sides are constant.The shadows of the fence and of the pole, both form two rectangle triangle. The first triangle, the smaller one, has a base of 7 feet (the shadow of the fence), and a height of 4 feet (the corresponding height of the fence)The second one, a bigger one, has a base of 26 feet (the shadow of the flagpole), and an unknown height (the height of the pole that its worrying you).Then, as stated, the proportion for both triangles remains constant. So: , where x is the height of the pole.x is solved as: . Meaning that the flagpole has 14.85 feet of height.Then when the height is compared to the distance from its base to your home, it is found that the pole is shorter then, there is no risk of the pole falling into your house.  

Period is the time it takes for one “cycle” to complete. in the parent sine function, period is 2*pi since sin(0) = 0, sin(pi/2) = 1, sin(pi) = 0, sin(3pi/2) = -1, and sin(2pi) = 0. at that point, the sequence repeats itself. i’m not sure if your graph is similar to the sine function since you didn’t provide a picture, but you can find the period by looking at a graph.