Question

$\color{blue}If \\ \: \boxed{x \: \cos A = 8 \: and \: 15 \: \cosec A = 8 \: then \: find \: \color{red}x }$
Quality answers needed..​

Answer 1

★ Given:

$x \: \cos A = 8 \: and \: 15 \: \cosec A = 8 \: then \: find \: \color{red}x$

Solution:

$➟x \cos A= 8$

$➟ \cos A = \frac{8}{x} = \color{red}\frac{adj.side}{hypo}$

$➟15 \: cosec A = 8 \sec A$

$➟ \frac{cosecA}{secA} = \frac{8}{15}$

$➟\frac{ \frac{1}{ \sin A} }{ \frac{1}{ \cos A} } = \frac{8}{15}$

$➟ \frac{ \cos A}{sin A} = \frac{8}{15}$

$\boxed{we \: know \: that : }\\ \frac{cosA}{sinA } = cot A$

$➟cot A = \frac{8}{15} = \frac{adj.side}{hypo}$

BY USING PYTHAGORUS THEOREM:

$➟ \: {x}^{2} = {15}^{2} + {8}^{2}$

$➟ \: {x}^{2} = 225 + 64$

$➟ \: {x}^{2} = 289$

$➟ \: {x}^{2} \times x = 17 \times 17$

$\boxed{x = 17}$