0
$\begingroup$

I have this basic trigonometry question of finding the length of "x" in the triangle Finding X. I know one side of the triangle and the opposite angle, so I figured it should be a simple case of just filling in the equations of cosine. I've tried looking at other solutions of similar problems, but I can't wrap my head around how to apply their approach to my problem.

Sorry if this is way too basic, I notice it's been too long since I've used trig..

$\endgroup$
  • $\begingroup$ Use the tangent (or cotangent) instead of the cosine, since you aren't given the hypotenuse. $\endgroup$ – saulspatz Mar 14 at 14:10
  • $\begingroup$ Actually, according to your figure, you know two angles: the $6$-degree angle and the right angle. That is what makes this problem solvable. $\endgroup$ – David K Mar 14 at 14:12
  • $\begingroup$ This may be helpful in applying trigonometry to right triangles: intmath.com/trigonometric-functions/… $\endgroup$ – David K Mar 14 at 14:17
0
$\begingroup$

$$\tan \theta =\dfrac{\text{side opposite }\theta}{\text{side adjacent }\theta}$$

Here the $\text{side opposite }\theta$ to the angle of $6^{\circ}$ is $x$ and $\text{side adjacent }\theta$ is $3$.

$$\tan 6^{\circ}=\dfrac{x}{3}\implies x=3\tan6^{\circ}$$

You can leave it like that as $6^{\circ}$ is not a special angle, if however, you can use a calculator, simply feed in the expression to get $x \approx 0.315312705798$ and you're done.

$\endgroup$
  • $\begingroup$ Have a look at mathworld.wolfram.com/TrigonometryAnglesPi30.html $\endgroup$ – Claude Leibovici Mar 14 at 15:03
  • $\begingroup$ Thanks for the reference @ClaudeLeibovici I meant special angle in the sense those that're usually remembered by most people like $\{0, 30, 45, 60, 90\}$ for the acute angle case. A value like $\tan 6^{\circ}$ is best to be left computed than remembered. $\endgroup$ – Paras Khosla Mar 14 at 15:09
  • $\begingroup$ For sure, I agree ! But, it is nice to know that we have an exact result. Replace the $3$ meters by $12345678987654321$ km and we can produce the exact result say within an error of $10^{-10}$ microns ! Cheers :-) $\endgroup$ – Claude Leibovici Mar 14 at 15:14
  • $\begingroup$ Sure that is true @ClaudeLeibovici. Cheers $\endgroup$ – Paras Khosla Mar 14 at 15:15
  • $\begingroup$ Sure @ClaudeLeibovici "Numerical Efficiency is your main concern" :) $\endgroup$ – Paras Khosla Mar 15 at 6:17
0
$\begingroup$

Use tangent: $\tan 6°=\frac{x}{3} \rightarrow x=3\tan 6° \approx 0.32$

$\endgroup$

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.