Triangles

2010015203

Level: 
B
In a triangle with interior angles \( 30^{\circ} \), \( 60^{\circ} \) and \( 90^{\circ} \), the shortest side is \( 10\,\mathrm{cm} \) long. Find the length of its longest side.
\( 20\,\mathrm{cm} \)
\( \frac{20}{\sqrt3}\,\mathrm{cm} \)
\( 20\sqrt3\,\mathrm{cm} \)
\(15\,\mathrm{cm} \)

2010015202

Level: 
B
The ladder is leaning against the wall of a house. Its length is \( 5 \) meters. How high does the ladder reach if the angle between it and the wall is \( 45^{\circ} \)? (See the picture.)
\( \frac{5\sqrt2}{2}\,\mathrm{m} \)
\( \frac{5}{2}\,\mathrm{m} \)
\( \frac{5\sqrt3}{2}\,\mathrm{m} \)
\( \frac{10}{\sqrt2}\,\mathrm{m} \)

2010015201

Level: 
A
Interior angles of a triangle \( ABC \) are in the ratio \( \alpha:\beta:\gamma=3:5:7 \). Calculate the measures of these angles.
\( \alpha=36^{\circ};\ \beta=60^{\circ};\ \gamma=84^{\circ} \)
\( \alpha=30^{\circ};\ \beta=50^{\circ};\ \gamma=70^{\circ} \)
\( \alpha=16.5^{\circ};\ \beta=30^{\circ};\ \gamma=133.5^{\circ} \)
\( \alpha=84^{\circ};\ \beta=60^{\circ};\ \gamma=36^{\circ} \)

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 \(a\)?
\(5\sin{35^{\circ}}\,\mathrm{cm}\)
\(\frac{5}{\sin{35^{\circ}}}\,\mathrm{cm}\)
\(5\cos{35^{\circ}}\,\mathrm{cm}\)
\(\frac{5}{\cos{35^{\circ}}}\,\mathrm{cm}\)