Triangle PQR is equilateral. QA is perpendicullar to PR and B is the midpoint of QA.What is the length of PB ? QR=30

Since the triangle is equilateral, then the lengths of
it's sides are equal.

PQ = PR = QR = 30
units

Since QA is perpendicular to PR, then QA is the
height of the triangle PQR.

We'll consider the right angled
triangle QAR, whose right angle is A = 90 degrees, R = 60 degrees and QA is a cathetus
and QR=30 is the hypothenuse.

First, we'll compute the
length of QA:

sin R =
QA/QR

sin 60 = QA/30

QA =
30*sin 60

QA = 30*sqrt3/2

QA =
15*sqrt3

QA = 25.98

Since B is
the midpoint of QA, then QB = BA = 25.98/2

AB =
12.99

Now, we'll calculate PB from the right angled
triangle PAB, A=90 degrees, PB is the hypothenuse.

We'll
apply Pythagorean Theorem

PB^2 = PA^2 +
BA^2

PA = 30/2

PA =
15

PB^2 = 15^2 +
12.99^2

PB =
19.84