Question

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

Answer 1

Let x − 1 be the hypotenuse By applying Pythagoras theorem we get

𝐴𝐶² = 𝐴𝐵² + 𝐵𝐶²

𝑥² = (24)² + (7)²

𝑥² = 576 + 49 = 62.5

x = 25

${\displaystyle \sin \theta =\frac{AB}{AC}=\frac{24}{25}}$

${\displaystyle \cos \theta =\frac{BC}{AC}=\frac{7}{25}}$

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

${\displaystyle =\frac{31}{25}}$