Triangles

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.
\(14\, \mathrm{m}\)
\(13\, \mathrm{m}\)
\(16\, \mathrm{m}\)
\(15\, \mathrm{m}\)

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.
\(4.2\, \mathrm{m}\)
\(5.9\, \mathrm{m}\)
\(3.6\, \mathrm{m}\)
\(11.2\, \mathrm{m}\)

9000035008

Level: 
B
Sun shines to the road at the angle \(53^{\circ }22'\). An electric column near the road casts the shadow of the length \(4.5\, \mathrm{m}\). Find the height of the column and round your answer to the nearest meters.
\(6\, \mathrm{m}\)
\(3\, \mathrm{m}\)
\(4\, \mathrm{m}\)
\(5\, \mathrm{m}\)

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.
\(2^{\circ }10'\)
\(3^{\circ }10'\)
\(2^{\circ }20'\)
\(3^{\circ }20'\)

9000045702

Level: 
B
Given a right triangle \(ABC\) (see the picture). Find the valid relation between the angle \(\alpha \) and the sides of the triangle.
\(\mathop{\mathrm{tg}}\nolimits \alpha = \frac{a} {c}\)
\(\sin \alpha = \frac{a} {c}\)
\(\cos \alpha = \frac{b} {a}\)
\(\mathop{\mathrm{cotg}}\nolimits \alpha = \frac{b} {a}\)

9000045703

Level: 
B
Given a right triangle \(ABC\) with the right angle at $C$ and an altitude $v$ (see the picture). Find the valid relation between the angle \(\alpha \) and the lengths in the triangle.
\(\sin \alpha = \frac{v} {b}\)
\(\sin \alpha = \frac{v} {c}\)
\(\sin \alpha = \frac{a} {v}\)
\(\sin \alpha = \frac{c} {a}\)

9000045704

Level: 
B
Given a right triangle \(ABC\) with the right angle at $C$ and an altitude $v$ (see the picture). Find the valid relation between the angle \(\beta \) and the lengths in the triangle.
\(\sin \beta = \frac{v} {a}\)
\(\mathop{\mathrm{tg}}\nolimits \beta = \frac{a} {v}\)
\(\cos \beta = \frac{v} {a}\)
\(\mathop{\mathrm{tg}}\nolimits \beta = \frac{v} {a}\)