which sine ratios are correct for ∆PQR? Check all that apply

sin(p)=r/q
sin(p)=p/q
sin(q)=r/p
sin(r)=q/r
sin(r)=r/q

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jajumonac jajumonac · Answer 1 · 2020-03-26T02:26:22+01:00

Answer:

[tex]sin(P)=\frac{p}{q}\\ sin(R)=\frac{r}{q}[/tex]

Step-by-step explanation:

In the given graph, we have the right triangle PQR, where q is the hypothenuse and r and p are legs.

Now, if we want to the sin function of an angle, it would be like

[tex]sin(A)=\frac{opposite}{adjacent}[/tex]

That is, the sin of an angle is the quotient between its opposite leg and its adjacent leg.

So, in this case, if we apply this defintion to P and R angles, we have

[tex]sin(P)=\frac{p}{q}\\ sin(R)=\frac{r}{q}[/tex]

Therefore, the right choices are the second and the last option.

[tex]sin(P)=\frac{p}{q}\\ sin(R)=\frac{r}{q}[/tex]

nishantwork777 nishantwork777 · Answer 2 · 2021-10-26T08:17:36+02:00

As, the given triangle, ΔPQR, is a right angle triangle, so by using the trigonometric relations, The correct options are:

[tex]Sin (P)=\frac{p}{q} \\Sin(R)=\frac{r}{q}[/tex]

Given information:

The triangle PQR is given

Where q is the hypotenuse and r and p are legs.

As, the given triangle, ΔPQR, is a right angle triangle, so one can use the trigonometric relations.

Now according to the trigonometry

The value of

[tex]Sin(A)=\frac{\text{opposite}}{\text{adjacent}}[/tex]

Applying above expression in the given triangle

we get:

[tex]Sin (P)=\frac{p}{q} \\Sin(R)=\frac{r}{q}[/tex]

Hence the required solution is :

[tex]Sin (P)=\frac{p}{q} \\Sin(R)=\frac{r}{q}[/tex]

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