Triangles

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 \( BCA \)?
\( 27.51^{\circ} \)
\( 16.12^{\circ} \)
\( 30.13^{\circ} \)
\( 12.45^{\circ} \)

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.)
\(313\, \mathrm{m}\)
\(1975\, \mathrm{m}\)
\(317\, \mathrm{m}\)
\(78\, \mathrm{m}\)

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.
\(40.6^{\circ}\)
\(49.4^{\circ}\)
\(59.0^{\circ}\)
\(31.0^{\circ}\)

9000035001

Level: 
B
The angle of elevation of a straight road is \(3^{\circ }30'\). 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.)
\(122\, \mathrm{m}\)
\(276\, \mathrm{m}\)
\(98\, \mathrm{m}\)
\(49\, \mathrm{m}\)

9000035003

Level: 
B
The tree of the height \(12\, \mathrm{m}\) is observed from the place horizontal with the base of the tree. The angle of elevation is \(10^{\circ }\). Find the distance of the observer from the base and round to the nearest meters.
\(68\, \mathrm{m}\)
\(2\, \mathrm{m}\)
\(12\, \mathrm{m}\)
\(48\, \mathrm{m}\)

9000035004

Level: 
B
The triangle \(ABC\) has the angle \(\beta = 59^{\circ }\) and the side \(a = 14\, \mathrm{cm}\). Find the altitude \(v_{c}\) (the line segment which is perpendicular to the side \(c\) and joins the vertex \(C\) with the side \(c\)) and round to the nearest centimeters.
\(12\, \mathrm{cm}\)
\(7\, \mathrm{cm}\)
\(10\, \mathrm{cm}\)
\(23\, \mathrm{cm}\)