Triangles

1003077006

Level: 
B
Giving a right-angled triangle, the hypotenuse is \( 50\,\mathrm{cm} \) long, the perimeter of the triangle is \( 12\,\mathrm{dm} \) and its area is \( 600\,\mathrm{cm}^2 \). Find the measures of all interior angles of the triangle.
\( 90^{\circ};\ 36.87^{\circ};\ 53.13^{\circ} \)
\( 90^{\circ};\ 30.96^{\circ};\ 59.04^{\circ} \)
\( 90^{\circ};\ 38.65^{\circ};\ 51.35^{\circ} \)
\( 90^{\circ};\ 33.13^{\circ};\ 56.87^{\circ} \)

1103077004

Level: 
B
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: 
B
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.
\( 2.08\,\mathrm{cm} \)
\( 5.64\,\mathrm{cm} \)
\( 2.05\,\mathrm{cm} \)
\( 2.18\,\mathrm{cm} \)

1003021809

Level: 
B
\( ABC \) is a right-angled triangle with the right angle at vertex \( C \), side \( b=10\,\mathrm{cm} \) and the altitude to the hypotenuse \( v_c=5\,\mathrm{cm} \). Find the measure of the angle \( BAC \).
\( 30^{\circ} \)
\( 45^{\circ} \)
\( 60^{\circ} \)
\( 90^{\circ} \)

1103021808

Level: 
B
There is a cottage on the top of the mountain. From our site \( P \), \( 2\,\mathrm{km} \) as the crow flies from the cottage, we can observe the cottage to be at an angle of elevation of \( 30^{\circ} \). How many altitude meters do we still have to overcome to get to the cottage?
\( 1000\,\mathrm{m} \)
\( 1732\,\mathrm{m} \)
\( 2\,\mathrm{km} \)
\( 1155\,\mathrm{m} \)