Question

Patricia has a lawn, ABCD. She has placed a watering hose, BD, as shown below.
Part A: Patricia 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

@Mertsj can you help me?

Answer 2

@Robb828 , do you know pythagoras theorem?
a^2 + b^2 = c^2

Answer 3

yes i do

Answer 4

Yes, apply that and get length AD

Answer 5

I mean first find BD and then find AD

Answer 6

That is take triangle BCD and apply pythagoras theorem and get BD.

Then take triangle ABD and apply pythagoras theorem and find AD

Answer 7

so i do 30^2 + 16^2 = c^2

Answer 8

yes. so get the value of c^2.

Now take triangle ABD and apply

sin 60 = BD / AD

Answer 9

Sorry Initially I thought AD is given. But AD is not given and hence you cannot apply pythagoras theorem for ABD

Answer 10

so what i got was 1156 = c^2

Answer 11

Get c. Then\

sin (60) = c / AB

Answer 12

you lost me...

Answer 13

No I didn't c= sqrt(1156)
Now sin(60) = BD/ AB
Do you know trigonometry??

Answer 14

not that much

Answer 15

Then sin of any angle is

sin(A) = opposite side to A / Hypotenuse of triangle

Answer 16

Now you get it ??

Answer 17

yea

Answer 18

so....

Answer 19

Now apply this, we get

sin(60) = BD / AB

we know that
sin (60) = sqrt(3) / 2
BD = sqrt (1156)

Apply this and and get your AB

Answer 20

i got 34

Answer 21

@Robb828
BD= 34

Now you know \[\sin(60) = {\sqrt{3} \over 2}\]
\[{\sqrt{3} \over 2} = {34 \over AB}\]

\[AB = 34 * { 2 \over \sqrt{3}}\]

Answer 22

@Robb828 , make sure you practice trigonometry.

Answer 23

ok thanks for you help and trust me i will lol

Answer 24

yw :)

Answer 25

@shivam_bhalla i forgot to ask do i multiply those last two or just leave them like that??

Answer 26

@Robb828 , If you have a calcultor at home, then simplify it, else leave it that way

Answer 27

*calculator

Answer 28

ok i do thank you

Answer 29

yw :)

Answer 30

\[BD=\sqrt{30^2+16^2}=34\]

Answer 31

\[AD=\frac{34}{\sqrt{3}}=\frac{34\sqrt{3}}{3}\]

Answer 32

Triangle BCD is a right triangle with legs 30 and 16. Using the Pythagorean theorem I found the hypotenuse BD of that triangle. That hypotenuse BD is the long leg of the 30-60-90 right triangle BDA. AD is the short leg of that triangle. The short leg of a 30-60-90 triangle can be found by dividing the long leg by the square root of three.