Question

If $\tan \theta =\frac{12}{5}$, then $\cos \theta =$

• A. $0.384$
• B. $0.55$
• C. $0.1$
• D. $0.9$

Answer 1

The correct option is A $0.384$

In the right-angled triangle $ABC$ with angle $B=90$

$\Rightarrow A{C}^2=A{B}^2+B{C}^2$

$\Rightarrow A{C}^2=(12{)}^2+(5{)}^2$

$\Rightarrow A{C}^2=144+25$

$\Rightarrow A{C}^2=169$

$\Rightarrow AC=13$

Then $\cos \theta =\frac{Base}{hypotenuse}=\frac{BC}{AC}=\frac{5}{13}=.384$