Oblique Shock wave on a wedge

Wave angle can be found from $\theta -\beta -M$  diagram. For deflection angle $\theta =20^{\circ}$  and Mach number, $M_{1}=2.8$ , wave angle $\beta =39.5^{\circ}$.

Therefore, normal component of upstream Mach number,

$$M_{n1}=M_{1}Sin\beta = 2.8Sin\left ( 39.5^{\circ} \right )=1.78$$

From normal shock properties table, for $M_{n1}=1.78$,

$\frac{p_{2}}{p_{1}}=3.530,\frac{T_{2}}{T_{1}}=1.517,M_{n2}=0.6210$

Therefore, Downstream pressure, $$p_{2}=\left ( \frac{p_{2}}{p_{1}} \right )p_{1}=\left ( 3.530 \right )\left ( 1\,atm \right )=3.53\,atm$$

Downstream temperature, $$T_{2}=\left ( \frac{T_{2}}{T_{1}} \right )T_{1}=\left ( 1.517 \right )310=470.27\,K$$

Downstream Mach number, $$M_{2}=\frac{M_{n2}}{sin\left ( \beta -\theta \right )}=\frac{0.6210}{Sin\left ( 39.5-20 \right )}=1.86$$