Find the exact value of the expression using the provided information.
-An airplane flying faster than the speed of sound creates sound waves that form a cone. If vertex angle of the cone and $\mathrm { m }$ is the Mach number for the speed of the plane, then $\sin \frac { \theta } { 2 } = \mathrm { m }$ $( \mathrm { m } 1 )$. Find the Mach number to the nearest tenth if $\theta = 30 ^ { \circ }$.
A) $3.9$
B) $4.5$
C) $3.7$
D) 5

Question

Find the exact value of the expression using the provided information.
-An airplane flying faster than the speed of sound creates sound waves that form a cone. If vertex angle of the cone and $\mathrm { m }$ is the Mach number for the speed of the plane, then $\sin \frac { \theta } { 2 } = \mathrm { m }$ $( \mathrm { m } > 1 )$. Find the Mach number to the nearest tenth if $\theta = 30 ^ { \circ }$.
A) $3.9$
B) $4.5$
C) $3.7$
D) 5

Quizplus · Accepted Answer

The Mach number is given by $\mathrm { m } = \sin \frac { \theta } { 2 }$. If $\theta = 30 ^ { \circ }$, then $\sin \frac { \theta } { 2 } = \sin 15 ^ { \circ } = 0.2588$. Rounding to the nearest tenth, the Mach number is 3.9.

Find the Exact Value of the Expression Using the Provided m\mathrm { m }m

Find the Exact Value of the Expression Using the Provided $\mathrm { m }$