Question

Given $\text{15 cot A = 8}$. Find the value of $\sin A$ and $secA$.

Answer 1

Find the value of given trigonometric functions :

We are given with $\text{15 cot A = 8}$

$\text{⇒ cot A =}\frac{8}{15}$

We know that,

$$\begin{gathered} \cot \mathrm{A}=\frac{\mathrm{B}\left(\mathrm{Base}\right)}{\mathrm{P}\left(\mathrm{Perpendicular}\right)} \\ \Rightarrow \mathrm{P}=15,\mathrm{B}=8 \end{gathered}$$

From these values we will get the value of H ( Hypotenuse )

$$\begin{gathered} {\mathrm{H}}^2={\mathrm{P}}^2+\hspace{0.17em}{\mathrm{B}}^2 \\ {\mathrm{H}}^2={\left(15\right)}^2+{\left(8\right)}^2 \\ {\mathrm{H}}^2=225+64 \\ {\mathrm{H}}^2=289 \\ \mathrm{H}=17 \end{gathered}$$

Now we have to find values of $\sin A$ and $secA$ ,

We know that ,

$$\begin{gathered} \text{=sin A =}\frac{\mathrm{P}\left(\mathrm{Perpendicular}\right)}{\mathrm{H}\left(\mathrm{Hypotenuse}\right)} \\ =\sin \mathrm{A}=\frac{15}{17} \end{gathered}$$

Also we know that ,

$$\begin{gathered} \sec \mathrm{A}=\frac{\mathrm{H}\left(\mathrm{Hypotenuse}\right)}{\mathrm{B}\left(\mathrm{Base}\right)} \\ \sec \mathrm{A}=\frac{17}{8} \end{gathered}$$

Hence, the value of $\sin A$ and $secA$ are $\frac{15}{17}\mathrm{and}\frac{17}{8}$ respectively.