Triangles

1103021609

Level: 
B
Points \( A \), \( B \) and \( C \) lie on the circle \( k \). The line segment \( AC \) is the diameter of the circle and the lines \( AC \) and \( BC \) contain the angle of \( 60^{\circ} \). Calculate the length of \( AC \) if the length of \( BC \) is \( 10\,\mathrm{cm} \). (See the picture.)
\( 20\,\mathrm{cm} \)
\( 5\sqrt3\,\mathrm{cm} \)
\( 5\,\mathrm{cm} \)
\( 2\sqrt3\,\mathrm{cm} \)

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.
\( 141\,\mathrm{cm} \)
\( 115\,\mathrm{cm} \)
\( 51\,\mathrm{cm} \)
\( 96\,\mathrm{cm} \)

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.
\( 4.69\,\mathrm{m} \)
\( 7.39\,\mathrm{m} \)
\( 9.46\,\mathrm{m} \)
\( 3.70\,\mathrm{m} \)

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.
\( 32.98\,\mathrm{m} \)
\( 31.78\,\mathrm{m} \)
\( 31.44\,\mathrm{m} \)
\( 32.64\,\mathrm{m} \)

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.
\( 1151.75\,\mathrm{m} \)
\( 203.09\,\mathrm{m} \)
\( 35.27\,\mathrm{m} \)
\( 1134.26\,\mathrm{m} \)

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