C

1003077010

Level: 
C
In an isosceles triangle \( ABC \) the base \( AB \) has length \( 12\,\mathrm{cm} \). The altitude to the base \( v_c=8\,\mathrm{cm} \). Determine the length of the median drawn from a vertex at the base to the side.
\( \sqrt{97}\,\mathrm{cm} \)
\( \sqrt{93}\,\mathrm{cm} \)
\( \sqrt{87}\,\mathrm{cm} \)
\( \sqrt{83}\,\mathrm{cm} \)

1103077008

Level: 
C
Given a triangle \( ABC \), the length of the median from \( C \) is \( 9\,\mathrm{cm} \) and the length of the median from \( B \) is \( 6\,\mathrm{cm} \). Let \( T \) be the centroid, and \( S \) be the midpoint of \( AC \). The measure of the angle \( BTC \) is \( 120^{\circ} \). Find the length of the side \( AC \).
\( 4\sqrt7\,\mathrm{cm} \)
\( 2\sqrt7\,\mathrm{cm} \)
\( 2\sqrt{13}\,\mathrm{cm} \)
\( 4\sqrt{13}\,\mathrm{cm} \)

1103077004

Level: 
C
In a triangle \( ABC \), \( a=15\,\mathrm{cm} \), \( b=6\,\mathrm{cm} \) and the measure of the angle \( CAB \) is \( 120^{\circ} \). Which of the following numbers gives as accurately as possible the measure of the angle \( ABC \)?
\( 20.27^{\circ} \)
\( 25.66^{\circ} \)
\( 60^{\circ} \)
\( 30^{\circ} \)

1103077003

Level: 
C
In an isosceles triangle \( ABC \), the base \( AB = 6\,\mathrm{cm} \), the measure of the angle \( ABC \) is \( 20^{\circ} \). The angle bisector of the angle \( BAC \) intersects the side \( BC \) at a point \( K \). Find the length of the line segment \( BK \). Round the result to two decimal places.
\( 2.08\,\mathrm{cm} \)
\( 5.64\,\mathrm{cm} \)
\( 2.05\,\mathrm{cm} \)
\( 2.18\,\mathrm{cm} \)

1003021805

Level: 
C
In a triangle with interior angles \( 30^{\circ} \), \( 60^{\circ} \) and \( 90^{\circ} \), the longest side is \( 10\,\mathrm{cm} \) long. Find the length of its shortest side.
\( 5\,\mathrm{cm} \)
\( 5\sqrt3\,\mathrm{cm} \)
\( 3\,\mathrm{cm} \)
\( 8\,\mathrm{cm} \)