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# Right ABC has its right angle at C, BC=4 , and AC=8 .

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Right △ABC has its right angle at C, BC=4 , and AC=8 .

What is the value of the trigonometric ratio?

sin A=

tan B=

sec A=

Feb 1, 2020

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The sides are

BC=4

AC=8

AB=$$\sqrt{80}$$ (applying Pythagoras theorem,

$$\sqrt{(AC)^2+(BC)^2}=AB$$ "Addition since AB is the hypotenuse"

So we know the sides and they ask for trigonometric ratios

sin A =??

I assume A is angle "A"

$$sin(A)=\frac{opposite}{hypotenuse}$$

The opposite side to angle A is BC and the hypotenuse is AB

We know BC=4 and AB= $$\sqrt{80}$$

$$sin(A)=\frac{4}{\sqrt{80}}$$

Here is hints for the next 2 questions:

$$tan(B)=\frac{opposite}{adjacent}$$

$$sec(A)=\frac{hypotenuse}{adjacent}$$Proof: (Notice that $$sec(A)=\frac{1}{cos(A)}$$, we know that $$cos(A)=\frac{Adjacent}{Hypotenuse}$$ , substitute: $$sec(A)=\frac{1}{\frac{adjacent}{hypotenuse}}$$ Multiply the numerator and denominator by the hypotenuse, $$sec(A)=\frac{hypotenuse}{adjacent}$$

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Feb 1, 2020