Answer:
Step-by-step explanation:
step 1
Find PN
we know that
PN is a diameter
PS is a radius
so
step 2
Find the measure of arc MP
step 3
Find the measure of angle MNP
we know that
The inscribed angle measures half that of the arc comprising
substitute the value
step 4
Find the measure of angle MPN
we know that
The inscribed angle measures half that of the arc comprising
substitute the value
step 5
Find the measure of angle NMP
The sum of the internal angles of a triangle must be equal to 180 degrees
therefore
The triangle MNP is a right triangle
step 6
Find the length MN
In the right triangle MNP
substitute the values
