Question

Triangle P Q R is shown. Angle Q R P is a right angle. Angle R P Q is 30 degrees and angle P Q R is 60 degrees. Given right triangle PQR, which represents the value of sin(P)? StartFraction R P Over R Q EndFraction StartFraction R P Over P Q EndFraction StartFraction R Q Over P Q EndFraction StartFraction R Q Over P R EndFraction

Answer 1

Answer: option (c) $\frac{RQ}{PQ}$  

Step-by-step explanation:

Given data:

In ∆ PQR, we are given

∠QRP = 90°

∠RPQ = 30°

∠PQR = 60°

To find: value of sin (P)

Solution:

In ∆ PQR, using the trigonometry properties of a triangle, we get

sin (P) = $\frac{Perpendicular}{Hypotenuse}$

here on the basis of angle P,  

perpendicular = RQ

hypotenuse = PQ  

Therefore,  

sin (P)

= ½  …… [∵ angle P = 30°, sin(30°) = ½ ]

= $\frac{RQ}{PQ}$

Thus, the value of sin(P) is represented by option(c): $\frac{RQ}{PQ}$ .