B

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?
\( 1000\,\mathrm{m} \)
\( 1732\,\mathrm{m} \)
\( 2\,\mathrm{km} \)
\( 1155\,\mathrm{m} \)

1103021807

Level: 
B
An artillery battery is placed on a cliff. From the edge of the cliff \( 200\,\mathrm{m} \) high, the angle of depression to the ship on the sea is \( 10^{\circ} \). What is the distance \( d \) (see the picture) from the battery to the ship? Round the result to two decimal places.
\( 1151.75\,\mathrm{m} \)
\( 203.09\,\mathrm{m} \)
\( 35.27\,\mathrm{m} \)
\( 1134.26\,\mathrm{m} \)

1103021806

Level: 
B
The figure shows a water tower. From the site \( 85 \) meters away at a height of \( 1.2 \) meters, the measured angle of elevation of the top of the tower is \( 20^{\circ}30' \). Find the height of the tower. Round the result to two decimal places.
\( 32.98\,\mathrm{m} \)
\( 31.78\,\mathrm{m} \)
\( 31.44\,\mathrm{m} \)
\( 32.64\,\mathrm{m} \)

1103021804

Level: 
B
The roof shield has the shape of an isosceles triangle. The width of the shield is \( 12\,\mathrm{m} \) and the slope of the roof is \( 38^{\circ} \). Calculate the height of the shield. Round the result to two decimal places.
\( 4.69\,\mathrm{m} \)
\( 7.39\,\mathrm{m} \)
\( 9.46\,\mathrm{m} \)
\( 3.70\,\mathrm{m} \)

1003021803

Level: 
B
The ladder is leaning against the wall of a house. Its length is \( 6 \) meters. How high does the ladder reach if the angle between it and the wall is \( 30^{\circ} \)? (See the picture.)
\( 3\sqrt3\,\mathrm{m} \)
\( 3\,\mathrm{m} \)
\( 6\,\mathrm{m} \)
\( \frac{\sqrt3}2\,\mathrm{m} \)

1103021802

Level: 
B
The arms of a double ladder are \( 150\,\mathrm{cm} \) long. After opening the ladder (look at the picture) the arms contain an angle of \( 40^{\circ} \). Calculate the height of the opened ladder (the distance between the highest point of the ladder and the ground). Round the result to the nearest integer.
\( 141\,\mathrm{cm} \)
\( 115\,\mathrm{cm} \)
\( 51\,\mathrm{cm} \)
\( 96\,\mathrm{cm} \)

1103171502

Level: 
B
Current-Voltage characteristic of a conductor is a relationship, usually represented as a graph, between the current \( I \) through the conductor and the voltage \( U \) across the conductor. The picture shows two characteristics: of a metal conductor (red colour) and of an electrolytic conductor (black colour). At what voltages need to be conductors connected so that the current is the same in both of them?
\( 10\,\mathrm{V} \)
\( 16\,\mathrm{V} \)
\( 8\,\mathrm{V} \)
\( 9.5\,\mathrm{V} \)