Right

Determine angles of the right triangle with the hypotenuse c and legs a, b, if: 2a+5b=5.283c

Final Answer:

α =  79.3769 °
β =  10.6231 °
γ =  90 °

Step-by-step explanation:

2a  +5b = 5.283c  c=1 2a  +5b = 5.283 a2+b2 =1  a= 2 5.283 − 5 b​     22 (5.283 − 5 b)2​ +  b2 =1  (5.283−5b)2+22b2=22  (5.283−5 b)2+22 b2=22 29b2−52.83b+23.91=0  p=29;q=−52.83;r=23.91 D=q2−4pr=52.832−4⋅29⋅23.91=17.438576 D>0  b1,2​=2p−q±D​​=5852.83±17.44​​ b1,2​=0.910862±0.071999 b1​=0.982861243 b2​=0.838862895  A=arcsin(b1​)=arcsin0.9829≐1.3854 rad α=A→  °=A⋅ π180​   °=1.3854⋅ π180​   °=79.377  °=79.3769∘=79°22′37"

Our quadratic equation calculator calculates it.

β=90−α=90−79.3769=10.6231∘=10°37′23"
γ=90=90∘

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algebraplanimetricsbasic operations and conceptsgoniometry and trigonometryUnits of physical quantitiesGrade of the word problem

 
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