Question

Find the value of $\sin P$. $\vartriangle PQR$ is a right - angled triangle, right angled at R.

Answer 1

In $\vartriangle PQR$, $\angle R = {90^ \circ }$. We have to find the value of $\sin P$. We know that $\sin \theta = \dfrac{{Perpendicular}}{{Hypotenuse}}$.
Now, we can solve this problem easily.

Complete step by step answer:
We can draw figures based on the information given in question.

In$\vartriangle PQR$,
$\angle R = {90^ \circ }$
We have to find the value of $\sin P$.
Now, $\sin P$ $= \dfrac{{Perpendicular}}{{Hypotenuse}}$
From $\vartriangle PQR$, we have;
$RQ$ = perpendicular(P)
$PQ$= hypotenuse(H)
$\sin P$ $= \dfrac{P}{H}$
$\Rightarrow$ $\sin P$ $= \dfrac{{RQ}}{{PQ}}$

$\therefore$ We have the required value of sin P = $\dfrac{{RQ}}{{PQ}}$

Note:
In the above question we need to know the formula of sine. In the same way in trigonometry we have other functions such as sin, cos, tan, cosec, sec, cot. All of these trigonometric functions have different formulas. Lets see some more formulae;
$\cos \theta = \dfrac{{base}}{{hypotenuse}}$,
$\tan \theta = \dfrac{{perpendicular}}{{base}}$,
$\cos ec\theta = \dfrac{{hypotenuse}}{{perpendicular}}$,
$\sec \theta = \dfrac{{hypotenuse}}{{base}}$,
$\cot \theta = \dfrac{{base}}{{perpendicular}}$.
It seems difficult and confusing to learn these formulae. So, I would suggest that you make some mnemonics to learn them. One more thing I want to mention here is that the formula of cosec is opposite of sine, formula of sec is opposite of cos, formula of cot is opposite of tan. Now, it would be easy for you to learn. These are some basic but important formulas. Now, we will see some facts about right angled - triangle that is in right - angled triangle one angle is 90$^ \circ$another angle is labeled as $\theta$, then three sides are called - Base - adjacent (next to) the angle $\theta$, Perpendicular - opposite to angle $\theta$, Hypotenuse - it is the longest side. We use Pythagoras theorem to find the length of the side of a right - angled triangle.