I don't get this question

[ZephyrKai]

The question goes "In triangle PQR, where Q is the right angle, and cosR = 2/3, then r = √5." so is it asking for the length of r? If so, how is that meant to be done?

 

[Deleted member 4993]

The question goes:

"In triangle PQR, where Q is the right angle, and cosR = 2/3, then r = √5."

so is it asking for the length of r? If so, how is that meant to be done?

It is NOT asking you anything

- it is making a statement - GIVING you the length of 'r' (= √5).​

Conventionally, 'r' is the length of the side opposite to the vertex 'R' of the triangle.

 

[Steven G]

You need to read things more carefully. If they are asking you for r then you are done since they told you what r equals. If you used some formula or rule and came up with another value for r then you have to be wrong.

If I tell you that x=2 you can't come back and say x= 17. NO! x=2.

 

[pka]

The question goes "In triangle PQR, where Q is the right angle, and cosR = 2/3, then r = √5." so is it asking for the length of r? If so, how is that meant to be done?

If we are given that \(\Delta PQR\) is a right triangle and \(\cos(R)=\frac{2}{3}\) then \(m(\overline{RP})=3~\&~m(\overline{QP})=\sqrt 5\).
Note that \(\displaystyle \left( 2,~\sqrt 5,~3\right) \)\) form a Pythagorean triple. Thus the associated triangle is a right triangle.

 

[HallsofIvy]

This is more a matter of grammar than math! "In triangle PQR, where Q is the right angle, and cosR = 2/3, then r = √5." is NOT a question and it is NOT asking for any thing. If it is a math problem, please state it entirely.