B

2000005604

Level: 
B
A right-angled triangle \(ABC\) with the right angle at the vertex \(C\) is given in the picture. Calculate the height \(v_c\), if \(a=20\,\mathrm{cm}\) and \(\beta=50^{\circ}\).
\( 20\sin{50^{\circ}}\)
\( 20\cos{50^{\circ}}\)
\( 20 \mathop{\mathrm{tg}} {50^{\circ}}\)
\( \frac{20}{\sin{50^{\circ}}}\)

2000005603

Level: 
B
A right-angled triangle \(ABC\) with the right angle at the vertex \(C\) is given in the picture. Calculate the length of the side \(b\), if \(a=20\,\mathrm{cm}\) and \(\beta=34^{\circ}\).
\(b=\frac{20}{ \mathop{\mathrm{tg}} {56^{\circ}}}\,\mathrm{cm}\)
\(b=\frac{20}{ \mathop{\mathrm{tg}} {34^{\circ}}}\,\mathrm{cm}\)
\( b=20\sin{34^{\circ}}\,\mathrm{cm}\)
\( b=20\cos{34^{\circ}}\,\mathrm{cm}\)

2000005602

Level: 
B
A right-angled triangle \(ABC\) is given in the picture. Its hypotenuse is \(10\,\mathrm{cm}\) long and the measure of its internal angle \(\alpha\) is \(30^{\circ}\). What are the lengths of the legs in the triangle?
\( a=5\,\mathrm{cm}\), \( b=5\sqrt{3}\,\mathrm{cm}\)
\( a=5\sqrt{3}\,\mathrm{cm}\), \( b=5\,\mathrm{cm}\)
\(a=10\cos{30^{\circ}}\,\mathrm{cm}\), \(b=10\sin{35^{\circ}}\,\mathrm{cm}\)
\(a=\frac{\sin{30^{\circ}}}{10}\,\mathrm{cm}\), \(b=\frac{\cos{30^{\circ}}}{10}\,\mathrm{cm}\)

2000005601

Level: 
B
A right-angled triangle \(ABC\) with the right angle at the vertex \(C\) is given in the picture. The length of the side \(c\) is \(5\,\mathrm{cm}\) and the measure of the angle \(\alpha\) is \(35^{\circ}\). What is the length of the side \(a\)?
\(5\sin{35^{\circ}}\,\mathrm{cm}\)
\(\frac{5}{\sin{35^{\circ}}}\,\mathrm{cm}\)
\(5\cos{35^{\circ}}\,\mathrm{cm}\)
\(\frac{5}{\cos{35^{\circ}}}\,\mathrm{cm}\)

2000005507

Level: 
B
We cut two triangles from the rectangular plate so that the resulting trapezoid has an area of \(30\,\mathrm{cm}^2\). One of its bases is twice as long as the other. What is the area of the two triangles that are cut off?
\(10\,\mathrm{cm}^2\)
\(20\,\mathrm{cm}^2\)
\(5\,\mathrm{cm}^2\)
\(8\,\mathrm{cm}^2\)