It is rational/irrational
Let 2x – y = 3 ——— equation 1
Let x + 5y = 14 ——— equation 2
Making x the subject in eqn 1, = x = y + 3 / 2 ——— eqn 3
• Put eqn 3 in eqn 2
(y + 3 / 2) + 5y = 14
6y = 14 – 3/2
6y = 25/2
y = 25/12
• put y = 25/12 in eqn 3
x = (25/12 + 3/2)
x = 43/12
Answer:
![m\angle CDB=90\\m\angle CBD=90-\alpha\\m\angle BCD=\alpha\\\\m\angle CDA=90\\m\angle CAD=\alpha\\m\angle ACD=90-\alpha](https://tex.z-dn.net/?f=m%5Cangle%20CDB%3D90%5C%5Cm%5Cangle%20CBD%3D90-%5Calpha%5C%5Cm%5Cangle%20BCD%3D%5Calpha%5C%5C%5C%5Cm%5Cangle%20CDA%3D90%5C%5Cm%5Cangle%20CAD%3D%5Calpha%5C%5Cm%5Cangle%20ACD%3D90-%5Calpha)
Step-by-step explanation:
The triangles are drawn below.
CD is perpendicular to AB as CD is height to AB.
Therefore, angles
°
So, triangles ΔCBD and ΔCAD are right angled triangles.
Now, from the right angled triangle ΔABC,
![m\angle A+m\angle B =90\\\alpha+m\angle B=90\\m\angle B=90-\alpha](https://tex.z-dn.net/?f=m%5Cangle%20A%2Bm%5Cangle%20B%20%3D90%5C%5C%5Calpha%2Bm%5Cangle%20B%3D90%5C%5Cm%5Cangle%20B%3D90-%5Calpha)
From ΔCBD,
is same as
.
So, ![m\angle CBD=90-\alpha](https://tex.z-dn.net/?f=m%5Cangle%20CBD%3D90-%5Calpha)
![m\angle BCD+m\angle BDC =90\\m\angle BCD+90-\alpha=90\\m\angle BCD=\alpha](https://tex.z-dn.net/?f=m%5Cangle%20BCD%2Bm%5Cangle%20BDC%20%3D90%5C%5Cm%5Cangle%20BCD%2B90-%5Calpha%3D90%5C%5Cm%5Cangle%20BCD%3D%5Calpha)
Now, from ΔCAD,
is same as ![m\angle A](https://tex.z-dn.net/?f=m%5Cangle%20A)
So, ![m\angle CAD=\alpha](https://tex.z-dn.net/?f=m%5Cangle%20CAD%3D%5Calpha)
![m\angle CAD+m\angle ACD =90\\\alpha+m\angle ACD=90\\m\angle ACD=90-\alpha](https://tex.z-dn.net/?f=m%5Cangle%20CAD%2Bm%5Cangle%20ACD%20%3D90%5C%5C%5Calpha%2Bm%5Cangle%20ACD%3D90%5C%5Cm%5Cangle%20ACD%3D90-%5Calpha)
Hence, the unknown angles of both the triangles are:
![m\angle CDB=90\\m\angle CBD=90-\alpha\\m\angle BCD=\alpha\\\\m\angle CDA=90\\m\angle CAD=\alpha\\m\angle ACD=90-\alpha](https://tex.z-dn.net/?f=m%5Cangle%20CDB%3D90%5C%5Cm%5Cangle%20CBD%3D90-%5Calpha%5C%5Cm%5Cangle%20BCD%3D%5Calpha%5C%5C%5C%5Cm%5Cangle%20CDA%3D90%5C%5Cm%5Cangle%20CAD%3D%5Calpha%5C%5Cm%5Cangle%20ACD%3D90-%5Calpha)
Answer:
C is the answer.
Step-by-step explanation: