Calculating Land Plot Dimensions and Area Near the Nile River

let's go to for a abdullah owns a plot of land near the river nile in the form of quadrilateral abcd

the length of the size are a b equals 40 meters bc equals

150 meters cd equals 60 meters and a d equals 84 meters angle bad is a right triangle

90 degree this information is shown on the diagram show that bd

equals 93 meter correct to the nearest meter first of all we need to connect

this bd and we have this

right triangle a b d then we can use the pythagorean theorem

to figure out this uh bd so let's go to 4a bd squared

equals a b squared plus a d squared

so we plug in 40 squared plus 84 squared

therefore for bd equals square root 40 squared plus 84 squared

put it into calculator first of all clear the memory second plus 712

then make sure the mode is a in degree for angle

then we will do second x squared four t squared plus

84 square enter then

you will get the 93 to the nearest integers

so we will get that 93 meters then we will label here 93

for 4b calculate the angle bcd bcd is this one let's label as a theta

so first of all you need to define the variable latch angle b c d equals theta

since we know all the three sides for the triangle b c d we can use the cosine law to figure out

this theta so we will do the cosine theta equals

let's recall the cosine law for the cosine law you will see cosine c

equals here you have a squared plus b squared minus c square all over 2 times a times

b so for the corresponding size 93 you will need to do minus here so you

have 115 squared plus 60 squared minus 93 squared all over 2 times 115

times 60. so we go to calculator now you will do alpha y equals enter

then you have 1 1 5 squared

plus 60 squared then minus 93 squared

all over 2 times 115 times 60.

enter then you will do second cosine

pull this down enter parenthesis back enter

your angle will be 53 point degree

you can just write down the answer theta equals 53 on 7 degree

let's go to 4c find the

area of for a b c d for this uh area a b c d we have two triangles

so we can use the area for triangle is a one-half a b sine c we have a

b then sine c is a 90 degree for over here i can have this one a

b this theta we already get 53.7

so we can write down the area equals one-half

40 times 84 sine 90 that's

what but let's write this down plus one half times one one five times a

sixty and a sign fifty three point seven

after you put it into graphing calculator you will get 4460.4525

meter squared when you change it into three sig figs it will be four thousand four hundred

sixty meter squared let's go to 4d the formula that the ancient egyptians

used to ask me the area of quadrilateral abcd is this one abdullah uses this formula to estimate

the area of his plot of land calculate abdullah's estimation for the

area so for this area this is a for the

equals we just directly plug in number a b is a 40

plus cd is a 60 then times 80 that's 84

plus bc is 115 then over 4. so we go to alpha y equals enter

40 plus 60 then multiply by 84

plus 115 then divided by 4

enter 4975 let's go to for e

find the percentage error in abdullah's estimate for the percentage error

this is the formula given in the formula chart the e

is the exact value and v a is the approximate value of for v so

we know the percentage error here equals absolute value exact value

it will be the one we figure out that is a four four

six zero point four five twenty five and so on for

approximate value will be 4 9 75 for the absolute value this is the fact

you have a minus b that equals b minus a

in another words the absolute value of

exact value minus the approximate value equals the absolute value of approximate

value minus the exact value so it doesn't matter which one minus which one

for the numerator let me write down four four six zero point four five

twenty five minus four nine seventy five you have to pay more attention to

the denominator denominator you have to use the exact value

exact value will be four four six zero point five 25

let's go to calculator math number

enter get the absolute value alpha y equals enter

get a fraction so we drop this down minus

4975 all over four four

zero six all over four four six zero

point four five twenty five or 74

then enter multiply by 100 so that we can get the percentage

that will be 11.5 percent so answer will be

11.5 percent [Music]