$\"\"$

Find the angle $\"\"$ .

The equation is $\"\"$ .

Half-angle identity : $\"\"$ .

$\"\"$ .

Since the mach number describing a plane $\"\"$ s speed cannot be negative, $\"\"$ .

$\"\"$

Consider $\"\"$ .

Substitute the values of $\"\"$ in $\"\"$ .

$\"\"$

The mach number of the plane is about 3.2.

$\"\"$

a. $\"\"$ .

b. The mach number of the plane is about 3.2.