Question

please send me my answer step by step​

Answer 1

Answer:

The values of SinA and SecA are 15/17 and 17/8.

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Step-by-step explanation:

In the question, it is given that :

$\bf :\implies~~ 15~ CotA=8$

$\bf :\implies~~ CotA=\dfrac{8}{15}$

$\:$

Here, we know that :

$\bf :\implies~~ TanA=\dfrac{1}{CotA}$

So :

$\bf :\implies~~ TanA=\dfrac{1}{\dfrac{8}{15}}$

$\bf :\implies~~ TanA=\dfrac{15}{8}$

$\bf :\implies~~ TanA=\dfrac{15}{8}=\dfrac{Opp}{Adj}$

$\:$

Let's now, consider a ∆ABC by taking the opposite and adjacent sides as 15units and 8units from the ratio TanA.

So the triangle has :

• AB : Base : 8 units
• BC : Perpendicular : 15 units
• AC : Hypotenuse : ?

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From Pythagoras theorem, we get :

$\bf :\implies~~ (AB)^2+(BC)^2=(AC)^2$

$\bf :\implies~~ (8)^2+(15)^2=(AC)^2$

$\bf :\implies~~ \sqrt{64+225}=AC$

$\bf :\implies~~ \sqrt{289}=AC$

$\bf :\implies~~ AC = 17~ units$

$\:$

Now, let's find SinA :

$\bf :\implies~~ SinA=\dfrac{Opp}{Hyp}$

$\bf :\implies~~ SinA=\dfrac{BC}{AC}$

$\bf :\implies~~ SinA =\dfrac{15}{17}$

$\:$

Finally, finding SecA :

$\bf :\implies~~ SecA=\dfrac{Hyp}{Adj}$

$\bf :\implies~~ SecA=\dfrac{AC}{AB}$

$\bf :\implies~~ SecA=\dfrac{17}{8}$

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Some important formulae:

Some other trignometric ratios are :

$\bf :\implies~~ Cos\theta =\dfrac{Adj}{Hyp}$

$\bf :\implies~~ Cot\theta =\dfrac{Adj}{Opp}$

$\bf :\implies~~ Cosec\theta=\dfrac{Hyp}{Opp}$