Triangles

9000035009

Level: 
B
Two forces act on the body at one point. The force \(F_{1} = 760\, \mathrm{N}\) acts horizontally from left to the right and the force \(F_{2} = 28.8\, \mathrm{N}\) acts vertically from the top to the bottom. Find the angle between the horizontal direction and the direction of the resulting force and round your answer to the nearest degrees and minutes.
\(2^{\circ }10'\)
\(3^{\circ }10'\)
\(2^{\circ }20'\)
\(3^{\circ }20'\)

9000036101

Level: 
C
A \(3\, \mathrm{m}\) long rod is in a slant position with respect to the observer's eye: one end is in the distance \(20\, \mathrm{m}\) and the other one \(18\, \mathrm{m}\). Find the visual angle of the rod (the angle between the lines which connect the observer's eye and the ends of the rod) and round to the nearest degrees.
\(7^{\circ }\)
\(3^{\circ }\)
\(45^{\circ }\)
\(83^{\circ }\)

9000036102

Level: 
C
Three forces act on the same body in the same point and the total force on the body is zero (the forces cancel). The first two forces are \(8\, \mathrm{N}\) and \(10\, \mathrm{N}\) and the angle between these forces is \(55^{\circ }\). Find the third force.
\(16\, \mathrm{N}\)
\(15\, \mathrm{N}\)
\(17\, \mathrm{N}\)
\(18\, \mathrm{N}\)

9000036103

Level: 
C
Three forces \(F_{1}\), \(F_{2}\) and \(F_{3}\) act on the same body in the same point and the total force on the body is zero (the forces cancel). The first two forces are \(F_{1} = 8\, \mathrm{N}\) and \(F_{2} = 10\, \mathrm{N}\) and the angle between \(F_{1}\) and \(F_{2}\) is \(55^{\circ }\). Find the angle between \(F_{3}\) and \(F_{1}\). Round your answer to the nearest degrees.
\(149^{\circ }\)
\(125^{\circ }\)
\(55^{\circ }\)
\(30^{\circ }\)

9000036106

Level: 
C
Two straight roads go off from the crossing. The angle between directions of the roads is \(52^{\circ }18'\). A significant tree is on the first road in the distance \(250\, \mathrm{m}\) from the crossing. A rock with a beautiful view is on the second road in the distance \(380\, \mathrm{m}\) from the crossing. Find the direct distance (length of a line segment) from the rock to the tree and round your answer to nearest meters.
\(301\, \mathrm{m}\)
\(411\, \mathrm{m}\)
\(568\, \mathrm{m}\)
\(629\, \mathrm{m}\)

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.)
\(122\, \mathrm{m}\)
\(276\, \mathrm{m}\)
\(98\, \mathrm{m}\)
\(49\, \mathrm{m}\)

9000035007

Level: 
B
A roof gable has the shape of an isosceles triangle with the base of \(14\, \mathrm{m}\). The angle between the roof and the horizontal direction is \(31^{\circ }\). Find the height of the gable. Round your result to one decimal place.
\(4.2\, \mathrm{m}\)
\(5.9\, \mathrm{m}\)
\(3.6\, \mathrm{m}\)
\(11.2\, \mathrm{m}\)

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.
\(12\, \mathrm{cm}\)
\(7\, \mathrm{cm}\)
\(10\, \mathrm{cm}\)
\(23\, \mathrm{cm}\)

9000035006

Level: 
B
A ladder of the length \(15\, \mathrm{m}\) leans against a wall. The angle between the ladder and the horizontal direction is \(70^{\circ }\). Find the height of the top of the ladder and round your answer to the nearest meters.
\(14\, \mathrm{m}\)
\(13\, \mathrm{m}\)
\(16\, \mathrm{m}\)
\(15\, \mathrm{m}\)

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.
\(68\, \mathrm{m}\)
\(2\, \mathrm{m}\)
\(12\, \mathrm{m}\)
\(48\, \mathrm{m}\)