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Cake

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Submitted By Greenvirus
Words 373
Pages 2
Trigonometri projekt

Mahmud-Ironman
Magnyssen-Thor
Daniel-Captain America

Formelsamling

Median:
En median i en trekant, er den linje fra en vinkel, der rammer præcis midt på den modstående side.
Der kan derfor altid tegnes tre medianer i en trekant, én for hver side. Medianen halverer en side og udtrykkes derfor i forbindelse med den. Det hedder derfor eksempelvis medianen til side a.
Vinkelhalveringslinje
En vinkelhalveringslinje er, som navnet hentyder til, en linje, der halverer en vinkel. Til en hvilken som helst vinkel i hvilken som helst geometrisk figur, kan der tegnes en vinkelhalveringslinje. Således opstår to nye vinkler, der hver er halv så store som den oprindelige vinkel. Denne nye vinkel kan eventuelt igen halveres.
2
2
I figuren er vinkel B eksempelvis 88°. Ved at tegne en vinkelhalveringslinje vil de 2 nye vinkler hver være: 88° = 44°

Formel 1. Pythagoras a2+b2=c2 Vi udregner hypotenusen ved at indsætte talende i Pythagoras
32+42=c2
25 = c2 25 = c
5 = c

Formel 2. Areal
Vi tager Arealet af den overstående trekant ved at bruge areal formlen A= 12 * g * h
Hvor ”h” er højden og ”g” er grundlinjen.
A= 12 * 3 * 4
A = 6
Arealet er 6

Formel 3. Sinus relationerne
Vi har formlen . Vi har sider og vinklerne nok til at kunne finde ”b” og det gør vi ved at sætte talende ind.
3sin74 =bsin⁡(74)

Nu hvor talende er sat ind isolere vi ”b” for at finde dens side.

Sin74* 3sin74=b

b = 3
Siden b er 3

Geometri i den virkelig verden.

Eks 1. Vi bruger geometri i hverdagen til at måle højden på fx et træ.
Vi regner højden ved at lave en vinkelhalveringslinje fra vinkel A til siden a for at skabe en ret vinkel. Det vil sige at vinkel A er halveret og er blevet delt i 2 lige store vinkler.
Udregner ny vinkel A
C = 53,47°
A = 36,53° b = 3,36
C = 53,47°
A = 36,53° b = 3,36
73,06 / 2 = 36,53°
A = 36,53°

Nu finder vi c/højden ved hjælp af sinus.
Sin(<) = Modstående kateteHypotenusen

Sin(53,47) = c3,36

Sin(53,47) * 3,36 = c

2,7 = c = h

Nu har vi regnet frem til at højden er = 2,7

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