Question

if the value of sin theta =5/13 then the value of y=24 tan theta +13cos theta is equal to​

Answer 1

sin theta = 5/13

We need to calculate the value of y= 24 tan theta + 13 cos theta

Using the Triangle law we can fing the value of cos theta and tab theta

cos theta = 12/13

and tan theta = 5/12

So the value of y = 24*(5/12) + 13*(12/13)

                      y= 2*5 + 12

                       y= 10+12

                        y= 22

Therefore the answer will be 22.

Answer 2

$\huge{\bigstar}{ \green{ \mathfrak{ \underline{ \underline{Question}}}}}{\bigstar}$

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$If\: the\: sin \theta = \displaystyle{\frac{5}{13}} \: then \:what\: is \:the \:value\\ of \:y=24 tan \theta +13cos \theta$

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$\huge{\bigstar}{ \green{ \mathfrak{ \underline{ \underline{Answer}}}}}{\bigstar}$

$\boxed{\red{\bold{Using\: identity;}}}$

$\purple{\implies sin^2\theta + cos^2\theta = 1}$

${\purple{\implies}}\left( \displaystyle{\frac{5}{13}} \right)^2+ cos^2 \theta = 1$

$\purple{\implies}cos^2 \theta = 1 - \displaystyle{\frac{25}{169}}$

$\purple{\implies}cos^2 \theta = \displaystyle{\frac{169 -25}{169}}$

${\purple{\implies}}cos^2 \theta = \displaystyle{\frac{144}{169}}$

$\purple{\implies}cos^2 \theta = \left( \displaystyle{\frac{12}{13}} \right)^2$

$\boxed{\red{\bold{Taking\: square \: root:}}}$

$\purple{\implies}cos \theta = \displaystyle{\frac{12}{13}}$

$\boxed{\red{\bold{To \: find:}}}$

$\green{\implies 24 tan \theta + 13 cos \theta}$

$\green{\implies}24 \left( \displaystyle{\frac{sin \theta }{cos \theta}} \right) + 13 cos \theta$

$\green{\implies}24 \left( \displaystyle{\frac{\frac{5}{13}}{\frac{12}{13}}} \right) + 13 \times \displaystyle{\frac{12}{13}}$

$\green{\implies}24 \times \displaystyle{\frac{5}{12}} + 12$

$\green{\implies}10 + 12$

$\green{\boxed{\implies{\bold{22}}}}$

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