Question : If in a right-angled $ riangle P Q R$, $ an Q=\frac{5}{12}$, then what is the value of $\cos Q$?
Option 1: $\frac{12}{5}$
Option 2: $\frac{13}{5}$
Option 3: $\frac{12}{13}$
Option 4: $\frac{5}{13}$

Question

Question : If in a right-angled $ riangle P Q R$, $ an Q=\frac{5}{12}$, then what is the value of $\cos Q$?

Option 1: $\frac{12}{5}$

Option 2: $\frac{13}{5}$

Option 3: $\frac{12}{13}$

Option 4: $\frac{5}{13}$

Team Careers360 · Accepted Answer

Correct Answer: $\frac{12}{13}$

Solution :
Given, $ an Q = \frac{5}{12}$
We know, $ an heta = \frac{ ext{Perpendicular}}{ ext{Base}}$
Applying Pythagoras theorem,
$\small ext{Hypotenuse}^2 = ext{Perpendicular}^2+ ext{Base}^2$
⇒ $ ext{H}^2=5^2+12^2$
⇒ $ ext{H}^2 = 25 + 144$
⇒ $ ext{H}=\sqrt{169}$
⇒ $ ext{H} = 13\ ext{units}$
Now, $\cos heta = \frac{ ext{Base}}{ ext{Hypotenuse}}$
⇒ $\cos Q = \frac{12}{13}$
Hence, the correct answer is $\frac{12}{13}$.

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Question : If in a right-angled △PQR, tan⁡Q=512, then what is the value of cos⁡Q?Option 1: 125Option 2: 135Option 3: 1213Option 4: 513

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Question : If in a right-angled $△ P Q R$ , $\tan Q = \frac{5}{12}$ , then what is the value of $\cos Q$ ?
Option 1: $\frac{12}{5}$
Option 2: $\frac{13}{5}$
Option 3: $\frac{12}{13}$
Option 4: $\frac{5}{13}$