Question

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



Part A: Veronica 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've been on this question for awhile now i'm really stuck D: please help

Answer 2

Hi mich4563 :)

How are you friend? :D

Answer 3

I am good thank you xD just a little worried haha and you?

Answer 4

Let us start.

As we can see there are 2 90deg angles. One is angle C and others is angle ADB.

Can you see these two angles having 90 degrees?

Answer 5

I am also fine and shine buddy. Don't ever worry. Just believe on your self and do what ever you can do with your own knowledge then your result will always be better. Good luck.

Answer 6

Now tell me can you see those angles?

Answer 7

yes =]

Answer 8

OK good

Answer 9

If there are/is any 90 degree angle in the triangle then always remember we can use Pythagorean theorem.

Do you know what is Pythagorean theorem?

Answer 10

Yea =D

Answer 11

OK good.

As you can see in figure we have two right angled triangles. One is BCD and other is ADB. Right?

Answer 12

Yes =]

Answer 13

So First we have to find length of BD. Because BD is same to both right angled triangles. BD is the part of BCD and as well as ADB. Right?

Answer 14

Yea

Answer 15

Let us calculate BD from triangle BCD.

As we have two sides given in triangles BCD so we can use Pythagorean theorem.
\[\large hyp^2=perp^2+base^2\]
\[\large BD^2=BC^2+CD^2\]
\[\large BD^2=28^2+21^2\]
\[\large BD^2=784+441\]
\[\large BD^2=1225\]
Take square root on Both sides
\[\large \sqrt{BD^2}=\sqrt{1225}\]
\[\large BD=35\]

So we have calculated length of BD

Have you understood?

Answer 16

Okay I understood that =D

Answer 17

Now in triangle ADB we have two things. One is length BD=35 and other is angle A=60deg. Right?

Answer 18

Yes =]

Answer 19

So we can use any suitable ratio.

We will use \[\LARGE Tan \theta\]

Answer 20

\[\large tan\theta=\frac{perp}{Base}\]
\[\large tan\theta=\frac{BD}{AD}\]
\[\large AD=\frac{BD}{tan\theta}\]
\[\large AD=\frac{35}{tan(60)}\]
\[\large AD=\frac{35}{1.732}\]
\[\large AD=20.20\]

Here is the length which is required to Veronica :D

Good luck dear.

Answer 21

Thank you sooo much! I was wondering if you could help with another question? It's different from this but I was stuck on it for a while.

Answer 22

Post it dear. I will try.

Answer 23

Joe uses the following steps to construct a perpendicular line through a point C on a line segment.

Step 1: From point C, draw an arc intersecting the line segment in points A and B.
Step 2: Use a straightedge to draw an arc from point A, one above and the other below the line.
Step 3: Without changing the compass width, draw two arcs from point B, above and below the line segment.
Step 4: Label the point of intersection of the arcs above the line segment as Q and below the line as R.
Step 5: Using a straightedge, join points Q and R.

Part A: Which is the first incorrect step?
Part B: Using complete sentences, explain your answer for Part A.
Part C: Explain why a compass works for the construction done by Joe.

Answer 24

@mich4563 I suggest you to post it as a new post. Thanks

Answer 25

Okay =]