## Subject IV. (30 points)

A right-angled triangle $ABC\left(m \nless A=90^{\circ}\right)$ has legs $AB=3 m, AC=4 m$. At $A$, a perpendicular is raised to the plane $(ABC)$, and a segment $AD=1 m$ is taken on it. Find:
a) $d(A,(DBC))$;

b) The areas of triangles $DAB, DAC, DBC, ABC$;
c) $\sin (\angle((DBC);(ABC)))$.

Prof. Cristian Petru Pop, ISJ Cluj

All questions are mandatory. 10 points are awarded by default.

SUCCESS!

Effective working time - 3 hours.

## Grading Scale for 8th Grade (OLM 2014 - Local Stage)

## Default $10 p$
## Subject IV.

Correct drawing
a) $d(A,(D B C))=\frac{12}{13} ;$ (WITH JUSTIFICATIONS)
b) $A_{D A B}=1.5 m^{2}, A_{D A C}=2 m^{2}, A_{D B C}=6.5 m^{2}, A_{A B C}=6 m^{2}$
c) $\sin (\Varangle((D B C) ;(A B C)))=\frac{5}{13} \quad$ (WITH JUSTIFICATIONS)