Question

If 15 cot A = 8,find the values of sin A and secA.​

Answer 1

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$\begin{gathered}\sf\bullet 15cot\:A=8\\ \\ \sf\implies cot\:A=\dfrac{8}{15}\end{gathered}$

We have to find the value of sinA and secA

Let,

▼ Base=8

▼ Height=15

Now by Pythagoras

$\begin{gathered}\sf \bullet H{}^{2}=P{}^{2}+b{}^{2}\\ \\ \sf\implies H{}^{2}=(15){}^{2}+(8){}^{2}\\ \\ \sf\implies H{}^{2}=225+64\\ \\ \sf\implies H{}^{2}= 289\\ \\ \sf\implies H=\sqrt{289}\\ \\ \sf\implies H=17\end{gathered}$

Now we have

$\begin{gathered}\sf\bullet Hypotenuse (H)=17\\ \sf\bullet Base(B)=8\\ \sf\bullet Perpendicular (p)=15\end{gathered}$

• Hypotenuse(H)=17
• Base(B)=8
• Perpendicular(p)=15

We have to find

• SinA and secA

$\boxed{\sf{sinA=\dfrac{P}{H}}}$

$\sf →sinA=\dfrac{15}{17}$

$\boxed{\sf{secA=\dfrac{H}{B}}}$

$\sf →secA=\dfrac{17}{8}$