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

answer: 0+0=0

step-by-step explanation:

that is the only answer that can make 0

the ratio of white tiles to blue tiles is 48: 16. the ratio in it's simplest form is 3: 1.

step-by-step explanation:

ratio: take the first number and add a colon next to it, then add the second number after that. make sure the ratio order matches up with the written problem!

simplest form: we can simplify the ratio 48 : 16 by dividing both terms by the greatest common factor (gcf).

the gcf of 48 and 16 is 16.

divide both terms by 16:

48 ÷ 16 = 3

16 ÷ 16 = 1

reducing to simplest form:

48 : 16 = 3 : 1