In pyramid ABCP, point M is the midpoint of BC . The segment PM is perpendicular to the plane of the base and PM = 9 cm. The radius of the circle circumscribed around ∆ABC is 24 cm and m∠CAB = 30°. Find the length of edge PB .

The length of edge PB is 15 cm

Step-by-step explanation:

step 1

In the triangle BOC

Find the measure of angle BOC

see the attached figure to better understand the problem

we have that

m∠CAB = 30° -----> is a inscribed angle

so

solve for arc BC

substitute the given value

Remember that

-----> by central angle

so

step 2

Find the length side BC

we have that

----> the radius of the circle

so

That means

Triangle BOC is an equilateral triangle (the measure of the interior angles is equal to 60 degrees)

therefore

M is the midpoint side BC

so

step 3

Find the length of edge PB

Applying the Pythagorean Theorem

we have

substitute

linear pair postulates