Triangles

2010015308

Level: 
B
A roof gable has the shape of an isosceles triangle with the base of \(14\, \mathrm{m}\) and the height \(6\,\mathrm{m}\). What is the angle between the roof and the horizontal direction? (See the picture.) Round your result to one decimal place.
\(40.6^{\circ}\)
\(49.4^{\circ}\)
\(59.0^{\circ}\)
\(31.0^{\circ}\)

2010015307

Level: 
B
The angle of elevation of a straight road is \(9^{\circ }\). The distance between two places measured along the road is \(2\, \mathrm{km}\). For these places, find the difference in altitudes, i.e. the vertical distance, and round the result to the nearest meter. (See the picture.)
\(313\, \mathrm{m}\)
\(1975\, \mathrm{m}\)
\(317\, \mathrm{m}\)
\(78\, \mathrm{m}\)

2010015305

Level: 
B
In a triangle \( ABC \), \( a=15\,\mathrm{cm} \), \( c=8\,\mathrm{cm} \) and the measure of the angle \( CAB \) is \( 120^{\circ} \). Which of the following numbers gives as accurately as possible the measure of the angle \( BCA \)?
\( 27.51^{\circ} \)
\( 16.12^{\circ} \)
\( 30.13^{\circ} \)
\( 12.45^{\circ} \)

2010015301

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 cliff to the ship? Round the result to two decimal places.
\( 1134.26\,\mathrm{m} \)
\( 1151.75\,\mathrm{m} \)
\( 35.27\,\mathrm{m} \)
\( 203.09\,\mathrm{m} \)