Question

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

Answer 1

Let triangle ABC, right anlged at B

$15cotA=8$

$\therefore cotA=\frac{8}{15}$

$cot\theta =\frac{Adjacentside}{Oppositeside}$

$\therefore \frac{AB}{BC}=\frac{8}{15}$

$\therefore AB=8$ & $BC=15$

by Pythagoras theorem,

$A{C}^2=A{B}^2+B{C}^2$

$A{C}^2=8^2+{15}^2$

$A{C}^2=64+225$

$A{C}^2=289$

$AC=17$

$\therefore sinA=\frac{Oppositeside}{Hypotenuseside}=\frac{15}{17}$

$secA=\frac{Hypotenuseside}{Adjacentside}=\frac{17}{8}$