Question

If tan theta= 24/7, then find sin theta + cos theta

Answer 1

Tan theta = opposite / adjacent = 24/7
the other side ( hypotenuse ) = √ 24² + 7² = 25

Sin theta = opposite / hypotenuse = 24/25
cos theta = adjacent / hypotenuse = 7/25
adding both you get 31/25

Answer 2

Answer:

$\sin\theta+\cos \theta=\frac{31}{25}$

Step-by-step explanation:

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

To find : $\sin\theta+\cos \theta$ ?

Solution :

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

According to trigonometry properties,

$\tan\theta=\frac{P}{B}$

So, Perpendicular P=24 and Base B=7

The hypotenuse is $H=\sqrt{P^2+B^2}$

$H=\sqrt{24^2+7^2}$

$H=\sqrt{576+49}$

$H=\sqrt{625}$

$H=25$

We know,

$\sin\theta=\frac{P}{H}$

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

$\cos\theta=\frac{B}{H}$

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

Substitute in the expression,

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

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

$\sin\theta+\cos \theta=\frac{31}{25}$