Right

Determine angles of the right triangle with the hypotenuse c and legs a, b, if:

$3a+4b=4.9c$

Correct answer:

α =  64.6 °
β =  25.4 °
γ =  90 °

Step-by-step explanation:

$$\begin{gathered} 3a+4b=4.9c \\ c=1 \\ 3a+4b=4.9 \\ {a}^2+b^2=1 \\ a={\displaystyle \frac{4.9-4b}{3}} \\ {\displaystyle \frac{(4.9-4b{)}^2}{3^2}}+b^2=1 \\ (4.9-4b{)}^2+3^2{b}^2=3^2 \\ 25b^2-39.2b+15.01=0 \\ p=25;q=-39.2;r=15.01 \\ D=q^2-4pr=39.2^2-4\cdot 25\cdot 15.01=35.64 \\ D>0 \\ {b}_{1,2}={\displaystyle \frac{-q\pm \sqrt{D}}{2p}}={\displaystyle \frac{39.2\pm \sqrt{35.64}}{50}} \\ {b}_{1,2}=0.784\pm 0.119398492453 \\ {b}_1=0.903398492453 \\ {b}_2=0.664601507547 \\ \text{ Factored form of the equation: } \\ 25(b-0.903398492453)(b-0.664601507547)=0 \\ \alpha =\arcsin b=64.6^{\circ } \end{gathered}$$

$\beta =\arccos b=25.4^{\circ }$

$\gamma =90^{\circ }$

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