Question

Monica has a lawn, ABCD. She has placed a watering hose, BD, as shown below.



Part A: Monica plans to put a fence along the length AD of her lawn. What is the length of the fence required?
Part B: Using complete sentences, explain how you arrived at the answer for Part A.

Answer 1

i dont get it -.-

Answer 2

Well, basically, you want to find the length of the segment AD. We can see that AD is a leg in a 30-60-90 triangle, so if we know one of the other side lengths in that triangle, then we can find AD using the ratio of side lengths or trigonometry.
We just have to find that other side. Conveniently, we can also see that BD is the hypotenuse of another right triangle with the given leg measurements. So, we can find BD using Pythagorean Theorem and then that will give us the necessary information to find AD.

Answer 3

yeah i found that BD is 30 but i dont know how to get AD

Answer 4

There's two ways to get AD's measurement. The first way is by using trigonometric functions, like sine, cosine, and tangents.
We know that \(m \angle BAD\) is \(60^\circ\). It is in a right triangle, so we can use a trigonometric function to relate the sides. We know BD, and we want AD. Which trigonometric function will relate these two sides?