math ubd.pptx

8/10/2019 math ubd.pptx

1/43

TheEssence

of LearningTrigonomet

ryin our

Society

Math II UBD

Kar l E lv i s Esp inosa

K imber ly Cas ipeChar lean Lou ChuaJeany De l Rosar io


2/43

UNDERSTANDING CONCETS

Right Triangle Based Defnitiono Trigonometric unctions

!ythagorean Theorem

"ngle o Elevation

"ngle o Depression


3/43

RIG!T TRIANGLE "

BASED DE#INITION O#TRIGONOMETRIC#UNCTIONS


4/43

Right Triangle # " triangle that has one

angle that measures $% degrees

&ypotenuse ' the longest side o the righttriangle(

"d)acent side 'the side beside the anglegiven* note that hypotenuse +ill never be

the ad)acent side o the triangle(

,pposite side ' it is the side o thetriangle that is opposite to the anglegiven(


5/43

-ine ' used to fnd an angle that has a

given value or its opposite side andhypotenuse(

Cosine ' used to fnd an angle +ith agiven value or its ad)acent side andhypotenuse in a right triangle(

Tangent ' used to fnd an angle +ith agiven value or its opposite side andad)acent side(


6/43

Cosecant ' it is the opposite o a sine(

.sually defned as one/ 0over1 sine theta(

-ecant ' it is the opposite o cosine(

.sually defned as one/ 0over1 cosinetheta(

Cotangent ' the opposite o tangent+hich is defned as one/ 0over1 tangenttheta(


7/43


8/43

T!E $T!AGOREAN T!EOREM


9/43

amous theorem named ater the 2ree3mathematician and philosopher4 $T!AGORAS(

"The area of the square built upon thehypotenuse of a right triangle is equal tothe sum of the areas of the squares upon

the remaining sides.

c5 6 a57 b5


10/43

Ang%e ofE%e&ation


11/43

The angle bet+een the

imaginary line o sight and ahori8ontal line4 +here theob)ect is above the observer(


12/43

Ang%e ofDe'ression


13/43

The angle o depression isthe angle bet+een the

imaginary line o sight and ahori8ontal line4 +here theob)ect is belo+ the observer(


14/43


15/43

Structures

an(Scenarios


16/43

Lan(mar)

* anaa(Sta(ium The stadium has

9:4:%% seats4but holds5%4%%% people+ith standingareas( ;t islocated at "li)is4Bacolod City(


17/43

SCENARIO

The girl on the bridge is s loo3ing do+n at the boy

??(=$ t a+ay rom the bridge at an angleo =:o( &o+ tall +ould she be rom theground i she>s standing on the bridge@


18/43


19/43

Commercia%

Bui%(ing

The L> fsher

hotel islocated at 9


20/43

SCENARIO

The girl across L> fsher hotel +hostands


21/43


22/43

Bas)et-a%% Ring

Stan(* TCS Bas)et-a%%Court

TrinityChristian-chool islocated at illa

"ngela -ubd(4Brgy(illamonteBacolod City(


23/43

SCENARIO" boy standing


24/43


25/43

COMUTATIONS


26/43

anaa( Sta(ium


27/43


28/43

L+,sher !ote%


29/43


30/43

TCS Bas)et-a%% Court


31/43


32/43

IMORTANCE


33/43

!anaad -tadium

Economic Im'act.

The height o the bridge has limitations in termso the height o some vehicles passing under it(

"s +e all 3no+ !ublic .tility ehicles4 !ublic.tility Jeepneys and !rivate ehicles do vary insi8es because o its designated design thusgiving them an advantage to pass under thebridge( ;n the case o the bridge in the !anaad

tadium not all vehicles can pass by4 duringevents li3e !anaad -a Aegros +here people bringtheir amilies in buses and other large vehicles(


34/43

-olution

or the beneft o all the vehicles4 i thebridge +as built a bit higher4 it canaccommodate all vehicles( Trac +ouldn>tarise or the mere act that truc3 driversand bus drivers +ould not have hesitationsto pass under it because they 3no+ thebridge is capable o letting them pass due

to its taller height(


35/43

L>fsher &otel Economic Im'act.

Due to the alluring impact and good amenities o

L Ffsher hotel it became +ell 3no+n here in Bacolod City(

Every Gass3ara estival4 it>s easy access to diHerentplaces made it more convenient to stay +ith( The taIthat this building pays add up to the taIes that ourgovernment has that +ould defnitely be converted tounds or the diHerent pro)ects o our government or the

betterment o our country( Though L> fsher>s location isvery accessible4 the place +here it is located isbecoming congested because other ne+ commercialbuildings that +ere built near there is causing trac onthe Lacson street itsel(


36/43

So%ution.

;t is better or the hotel to relocate i everthey still have plans in eItending and

improving their appearance( Though i everthey do relocate4 they should also reconsiderthe accessibility o their customers i theystill +ant to continue in the business section

o our society(


37/43

TC- Bas3etball Court

Economic impact

The structure +as +ell built4 since the ring is instandard height and the court is +ide( The structure isadvantageous or events li3e riendly matches andsports ests because it can hold t+o gamessimultaneously(

-olution

The school should host riendly matches to ma3e useo the +ell# built court(


38/43

CONCLUSION

e have concluded that using trigonometry0trigonometric unctions14 especially the righttriangle4 !ythagorean Theorem4 and the angles

o elevation and depression could be o greathelp in determining un3no+n distances andangles o various structures +hen instrumentsand tools or measuring become inaccessibleand unavailable( "nd also by usingtrigonometric unctions4 measuring +ould be alot aster and easier than using the manual +ayo measuring(


39/43

RECOMMENDATION

e recommend the use o other techniuesand methods or measuring( .sing tools that+ould +or3 better than clinometers are highly

recommended( "nd also in terms o measuring4more accurate measurements o the parts areimportant in determining the right measuremento the +hole structure( The more accurate you are

+ith your measurements4 the more li3ely you +illcome up +ith the correct results(


40/43

RE#LECTION

;n this .BD pro)ect +e have learned that it ta3est+o to tango to fnish any feld +or3( Camaraderieand patience +ere the main actors +hy +e have

fnished this study in right time( e also learned toappreciate the beauty o trigonometry or it toachieve such brilliant ideas li3e that( ;trigonometry +asn>t discovered inrastructuressuch as home4 commercial buildings and landmar3+ouldn>t arise( ;ndeed4 Trigonometry becomes veryuseul and handy +hen tools or measuring areunavailable( Trig( is )ust simply ama8ing


41/43

DOCUMENTATION


42/43


43/43

T!E END

Documents

math ubd.pptx