Right Triangle Calculations

We know the right angle γ, side b = 14 cm, and height vc = 8.8 cm in the right triangle ABC. Calculate:
angle α =
angle β =
side a =
side c =

Final Answer:

A =  38.9448 °
B =  51.0552 °
a =  11.3147 cm
c =  18.0006 cm

Step-by-step explanation:

$$\begin{gathered} b=14\text{cm} \\ v=8.8\text{cm} \\ \sin A=v/b \\ A=\frac{180°}{\pi }\cdot \arcsin (v/b)=\frac{180°}{\pi }\cdot \arcsin (8.8/14)=38.9448^{\circ }=38°56^{\prime }41" \end{gathered}$$

$B=90-A=90-38.9448=51.0552^{\circ }=51°3^{\prime }19"$

$$\begin{gathered} \sin B=v/a \\ a=v/\sin (B°\to \text{rad})=v/\sin (B°\cdot \frac{\pi }{180})=8.8/\sin (51.055196405904°\cdot \frac{3.1415926}{180})=11.315=11.3147\text{cm} \end{gathered}$$

$c=\sqrt{a^2+b^2}=\sqrt{11.3147^2+14^2}=18.0006\text{cm}$

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