Question

In circle S,diameter PN is drawn .If measurement arc MN=110 degrees and PS=10 then find the length of MN to the nearest tenth.Show how you found your answer

Answer 1

Answer:

$MN=16.4\ units$

Step-by-step explanation:

step 1

Find PN

we know that

PN is a diameter

PS is a radius

$PS=10\ units$

so

$PN=2*PS=2*10=20\ units$

step 2

Find the measure of arc MP

$arc\ MN+arc\ MP=180\°$

$arc\ MN=110\°$

$arc\ MP=180\°-110\°=70\°$

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

$sin($

substitute the values

$sin(55\°)=\frac{MN}{20}$

$MN=(20)sin(55\°)=16.4\ units$