Question

given 15 cot A = 8 find sin square A​

Answer 1

Answer:

17

15

Step-by-step explanation:

Given,

15cotA=8

cotA=

15

8

=> tanA=

8

15

-------(tanA=

cotA

1

)

We know that,

tanθ=

adjacentSide

oppositeSide

Consider the attached figure, triangleABC

From Pythagoras theorem,

AC

2

=AB

2

+BC

2

AC

2

=8

2

+15

2

=64+225=289

AC=17

cosA=

Hypotenuse

adjacentSide

=

AC

AB

=

17

8

secA=

cosA

1

=

17

8

1

8

17

sinA=

Hypotenuse

oppositeSide

=

AC

BC

=

17

15

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Answer 2

$\large{ \bold{ \cot( \alpha ) = \frac{8}{15} }}$

$\large{ \bold{1 + { \cot( \alpha ) }^{2} = { \csc( \alpha ) }^{2} }}$

$\large{ \bold{1 + \frac{64}{225} = { \csc( \alpha ) }^{2} }}$

$\large{ \bold{ \frac{225 + 64}{225} = { \csc( \alpha ) }^{2} }}$

$\large{ \bold{ \frac{289}{225} = { \csc( \alpha ) }^{2} }}$

$\large{ \bold{ \pink{ { \sin( \alpha ) }^{2} = \frac{225}{289} }}}$