Question

tantheta =8/15
find sintheta and cos theta


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Answer 1

Answer :

$\sf\red {\longrightarrow \: \sin \theta = \dfrac{8}{17} }$

$\sf \red {\longrightarrow \: \cos \theta = \dfrac{15}{17} }$

Given :

$\odot \: \sf{ \tan \theta = \dfrac{8}{15} }$

To find :

$\odot \: \sf{ \sin \theta \: and \: \cos \theta }$

Calculation :

As we know that,

$\sf {\longrightarrow \: \tan \theta = \dfrac{Perpendicular}{Base} }$

So, according to the question :

$\sf {\longrightarrow \: \tan \theta = \dfrac{P}{B}= \dfrac{8}{15}}$

• Perpendicular = 8
• Base = 15

Also, we know that :

$\sf {\longrightarrow \: \sin \theta = \dfrac{Perpendicular}{Hypotenuse} }$

$\sf {\longrightarrow \: \cos \theta = \dfrac{Base}{Hypotenuse} }$

By pythagoras property, we'll calculate the hypotenuse :

We know that,

→ H² = B² + P²

→ H² = (15)² + (8)²

→ H² = 225 + 64

→ H² = 289

→ H = √289

→ H = 17

Henceforth,

$\sf {\longrightarrow \: \sin \theta = \dfrac{Perpendicular}{Hypotenuse} }$

$\sf\red {\longrightarrow \: \sin \theta = \dfrac{8}{17} }$

$\sf {\longrightarrow \: \cos \theta = \dfrac{Base}{Hypotenuse} }$

$\sf \red{\longrightarrow \: \cos \theta = \dfrac{15}{17} }$