Question

Determine o valor das seguintes razões trigonométricas

OBS:só quero saber a B,C e F​

Answer 1

Explicação passo-a-passo:

b) Seja a = AC

$\sf sen~\hat{A}=\dfrac{cateto~oposto}{hipotenusa}$

$\sf \dfrac{7}{25}=\dfrac{7}{a}$

$\sf a=25$

Seja b = AB. Pelo Teorema de Pitágoras:

$\sf b^2+7^2=25^2$

$\sf b^2+49=625$

$\sf b^2=625-49$

$\sf b^2=576$

$\sf b=\sqrt{576}$

$\sf b=24~cm$

Logo:

$\sf tg~\hat{C}=\dfrac{cateto~oposto}{cateto~adjacente}$

$\sf \red{tg~\hat{C}=\dfrac{24}{7}}$

c)

Seja a = DF

$\sf cos~\hat{D}=\dfrac{cateto~adjacente}{hipotenusa}$

$\sf\dfrac{20}{29}=\dfrac{20}{a}$

$\sf a=29~cm$

Logo:

$\sf sen~\hat{D}=\dfrac{cateto~oposto}{hipotenusa}$

$\sf \red{sen~\hat{D}=\dfrac{21}{29}}$

f) Seja b = GI

$\sf tg~\hat{C}=\dfrac{cateto~oposto}{cateto~adjacente}$

$\sf \dfrac{3}{4}=\dfrac{b}{24}$

$\sf 4b=3\cdot24$

$\sf 4b=72$

$\sf b=\dfrac{72}{4}$

$\sf b=18~cm$

Seja a = GH. Pelo Teorema de Pitágoras:

$\sf a^2=18^2+24^2$

$\sf a^2=324+576$

$\sf a^2=900$

$\sf a=\sqrt{900}$

$\sf a=30~cm$

Logo:

$\sf sen~\hat{H}=\dfrac{cateto~oposto}{hipotenusa}$

$\sf sen~\hat{H}=\dfrac{18}{30}$

$\sf \red{sen~\hat{H}=\dfrac{3}{5}}$