1
$\begingroup$

There is an angle equal 0.54 radians and opposite leg equal to 3 units, I need to find the length of the adjacent leg. I know that I have to do ${\rm leg} = \frac{3}{\tan(0.54 \text{ rad})}$.

I got this task from books and there is the determination $0.54 \text{ rad} = \frac{3}{5}$ but there isn't any description how to get result from 0.54 radian to $\frac{3}{5}$. I tried to find $0.54 \text{ rad} = \frac{54}{100} = \frac{27}{50}$ but I couldn't do it. How can I get $\frac{3}{5}$ from 0.54 radian or from another number, for example 0.36? I found answer here, but I couldn't understand because I go to school and didn't find description such method in book my level

update I know answer, I understand solving, but I can't understand how to get $\frac{3}{5}$ from $0.54 \text{ rad}$.

$\endgroup$
5
  • $\begingroup$ The tangent of an angle is equal to the opposite side divided by the adjacent side. Can you see how to get $\frac{3}{5}$ now? $\endgroup$
    – Florian D'Souza
    Dec 27, 2014 at 22:07
  • 1
    $\begingroup$ 5 is the length of adjacent leg $\endgroup$
    – Irrational Person
    Dec 27, 2014 at 22:11
  • $\begingroup$ @FlorianD'Souza, No. $\endgroup$
    – volkov
    Dec 27, 2014 at 22:56
  • $\begingroup$ To compute the sine, cosine, or tangent of an arbitrary angle by hand can be a long and laborious procedure. That is why they used to teach students how to look up the answer in a printed table of the functions--although or course someone else had to go to great trouble to create those tables. Are you asking about the details of such procedures? $\endgroup$
    – David K
    Dec 28, 2014 at 4:01
  • $\begingroup$ @DavidK, yes, I know it is Taylor series $\endgroup$
    – volkov
    Dec 28, 2014 at 18:01

3 Answers 3

Reset to default
4
$\begingroup$

$\tan(0.54)=0.5994..\approx \frac{3}{5}$ where the angle is in radian.

An approximation is the best you can do since $\tan(x) \not\in \mathbb{Q}$ if $x\ne0$ and $x \in \mathbb{Q}$ see this question and answers

$\endgroup$
2
  • 1
    $\begingroup$ he already answered it $\endgroup$
    – Irrational Person
    Dec 27, 2014 at 23:03
  • $\begingroup$ @Bot, sorry, I understood. thanks $\endgroup$
    – volkov
    Dec 27, 2014 at 23:23
2
$\begingroup$

We know that one way to find the tangent of an angle is to divide the opposite side by the adjacent side. Therefore, we have:

$$\tan(0.54) = \frac{3}{x}$$ where x is the unknown length of the adjacent side. We can then solve for x:

$$x= \frac{3}{\tan(0.54)}$$ which is equal to 5.005 (approximately).

$\endgroup$
0
1
$\begingroup$

adjacent leg = 3/tan(angle)

$\text{adjacent leg} = \frac{3}{tan(0.54rad)} = 5$

check

$$ \tan^{-1}\left(\frac{3}{5}\right) = .54\text{rad}$$

//EDIT

CHECK

$5 * \tan(0.54\text{rad}) = 3$

because $ 5 * \frac{3}{5} = 3$

we can concluding that

$\tan(.54\text{rad}) = \frac{3}{5}$

$\endgroup$
0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.