Question

What is the approximate length of RP? Round to the nearest tenth.

Answer 1

Use Pythagorean Theorem:
c = sr (a^2 + b^2) = sr (3^2 + 5.3^2)
= sr (9 + 28.09) = sr (37.09)
= 6.09 = 6.1

Answer 2

Answer:  $6.1\text{ units}$

Step-by-step explanation:

Given: Tangent $\overline{QR}$ is tangent to circle P at point Q.

We know that the radius from the center of the circle to the point of tangency is perpendicular to the tangent line.

Therefore,Tangent $\overline{QR}$ is perpendicular to radius QP at point of tangency Q.

Then, the triangle formed by Tangent and radius must be aright triangle.

So by Pythagoras theorem, we have

$\overline{RP}^2=\overline{RQ}^2+\overline{QP}^2\\\\\Rightarrow\overline{RP}^2=(5.3)^2+(3)^2\\\\\Rightarrow\overline{RP}^2=37.09\\\\\Rightarrow\overline{RP}=\sqrt{37.09}=6.09015599143\approx6.1\text{ units}$

Hence, the approximate length of $\overline{RP}=6.1\text{ units}$