Question

special right triangles find the values of the variables answers must be in simplest form

Answer 1

For right triangles we can use trigonmoetrical ratios if we want calculate the oppisite side of an angle

on this case we use sine to calculate m

$\sin (\alpha)=\frac{O}{H}$

where alpha is the angle, O the opposite side of the angle and H the hypotenuse of the triangle

on this triangle

alpha is 45°

the front side is m

and the hypoteuse 7

so replacing

$\sin (45)=\frac{m}{7}$

on this point we can solve m form the equation and calulate

$\begin{gathered} m=7\sin (45) \\ m=\frac{7\sqrt[]{2}}{2} \\ \\ m\approx4.95 \end{gathered}$