Triangles

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

1003021805

Level: 
B
In a triangle with interior angles \( 30^{\circ} \), \( 60^{\circ} \) and \( 90^{\circ} \), the longest side is \( 10\,\mathrm{cm} \) long. Find the length of its shortest side.
\( 5\,\mathrm{cm} \)
\( 5\sqrt3\,\mathrm{cm} \)
\( 3\,\mathrm{cm} \)
\( 8\,\mathrm{cm} \)

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

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

1003076909

Level: 
B
\( ABC \) is a triangle. Given \( |AB|=3\,\mathrm{cm} \), the measure of \( \measuredangle CAB \) is \( 75^{\circ} \), and the measure of \(\measuredangle ABC \) is \( 45^{\circ} \), calculate the length of the side \( AC \).
\( \sqrt6\,\mathrm{cm} \)
\( 3\sqrt2\,\mathrm{cm} \)
\( 2\sqrt3\,\mathrm{cm} \)
\( 3\frac{\sqrt3}{\sqrt2}\,\mathrm{cm} \)

1103076908

Level: 
B
The area of an obtuse triangle is \( 4\,\mathrm{cm}^2 \) and the lengths of the sides containing the obtuse angle are \( 2\,\mathrm{cm} \) and \( 8\,\mathrm{cm} \). Give the measure of this angle.
\( 150^{\circ} \)
\( 120^{\circ} \)
\( 135^{\circ} \)
\( 105^{\circ} \)