Question : If $\theta$ is an acute angle and $\sin \theta=\frac{21}{25}$, then what is the value of $\tan \theta$?
Option 1: $\frac{2 \sqrt{46}}{21}$
Option 2: $\frac{25}{2 \sqrt{46}}$
Option 3: $\frac{21}{2 \sqrt{46}}$
Option 4: $\frac{2 \sqrt{46}}{25}$
New: SSC CHSL Tier 2 answer key released | SSC CHSL 2024 Notification PDF
Recommended: How to crack SSC CHSL | SSC CHSL exam guide
Don't Miss: Month-wise Current Affairs | Upcoming government exams
Correct Answer: $\frac{21}{2 \sqrt{46}}$
Solution :
Given, $\theta < 90°$ and $\sin \theta=\frac{21}{25}$
We know, $\sin\theta = \frac{\text{Perpendicular}}{\text{Hypotenuse}}$
⇒ Perpendicular = 21 and Hypotenuse = 25
Using Pythagoras theorem,
Hypotenuse
2
= Perpendicular
2
+ Base
2
⇒ 25
2
= 21
2
+ Base
2
⇒ Base = $\sqrt{25^2-21^2}$
⇒ Base = $\sqrt{625-441}$
= $\sqrt{184}$
= $2\sqrt{46}$
Now, $\tan \theta=\frac{\text{Perpendicular}}{\text{Base}}=\frac{21}{2\sqrt{46}}$
Hence, the correct answer is $\frac{21}{2\sqrt{46}}$.
Related Questions
Know More about
Staff Selection Commission Combined High ...
Result | Eligibility | Application | Admit Card | Answer Key | Preparation Tips | Cutoff
Get Updates Brochure
Your Staff Selection Commission Combined Higher Secondary Level Exam brochure has been successfully mailed to your registered email id “”.
