Question

Is $\tan \theta =\frac{24}{7}$, find that $\sin \theta +\cos \theta$

Answer 1

Given,

$\tan \theta =\frac{24}{7}$

We know that,

$\tan \theta =\frac{oppositeSide}{adjacentside}$

$(Hypotenuse{)}^2=(oppositeSide{)}^2+(adjacentSide{)}^2$

$(Hypotenuse{)}^2=(24{)}^2+(7{)}^2$

$(Hypotenuse{)}^2=576+49=625$

$\left(Hypotenuse\right)=25$

We know that,

$\sin \theta =\frac{oppositeSide}{Hypotenuse}=\frac{24}{25}$

$\cos \theta =\frac{adjacentSide}{Hypotenuse}=\frac{7}{25}$

$\sin \theta +\cos \theta =\frac{24}{25}+\frac{7}{25}$

$=\frac{(24+7)}{25}$

$=\frac{31}{25}$