Right triangle

A right triangle ABC is given, c is a hypotenuse. Find the length of the sides a, b, the angle beta if c = 5 and angle alfa = A = 35 degrees.

Correct answer:

a =  2.8679
b =  4.0958
B =  55 °

Step-by-step explanation:

$$\begin{gathered} c=5 \\ A=35\text{ ° } \\ \sin A=a\mathrm{/}c \\ a=c\cdot \sin A\mathrm{°}=c\cdot \sin 35\mathrm{°}=5\cdot \sin 35\mathrm{°}=5\cdot 0.573576=2.868=2.8679 \end{gathered}$$

$$\begin{gathered} \cos A=b\mathrm{/}c \\ b=c\cdot \cos A\mathrm{°}=c\cdot \cos 35\mathrm{°}=5\cdot \cos 35\mathrm{°}=5\cdot 0.819152=4.09576=4.0958 \\ \text{ Verifying Solution: } \\ {b}_1=\sqrt{c^2-a^2}=\sqrt{5^2-2.8679^2}\doteq 4.0958 \end{gathered}$$

$B=90-A=90-35=55\text{°}$

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