Triangles
Right-Angled Triangles I
Submitted by vladimir.arzt on Thu, 10/17/2024 - 14:15Right-Angled Triangles II
Submitted by vladimir.arzt on Thu, 10/17/2024 - 13:512010015310
Level:
C
The shadow of a \(32\,\mathrm{m}\) high tree is \(40\) meters. At the same moment, the shadow of a person is \(200\,\mathrm{cm}\) long. What is the height of the person?
\(160\,\mathrm{cm}\)
\(170\,\mathrm{cm}\)
\(180\,\mathrm{cm}\)
\(185\,\mathrm{cm}\)
2010015309
Level:
B
The right angled triangle \(ABC\) is given (See the picture.). Choose the correct statement.
\(\mathrm{tg}\,\alpha = \frac{a}
{b}\)
\(\sin \beta= \frac{a}
{c}\)
\(\cos \beta = \frac{a}
{b}\)
\(\mathrm{tg}\,\beta = \frac{a}
{b}\)
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 \( BCA \)?
\( 27.51^{\circ} \)
\( 16.12^{\circ} \)
\( 30.13^{\circ} \)
\( 12.45^{\circ} \)
2010015306
Level:
B
The angles \( \alpha \), \(\beta \), \( \gamma \) of a right-angled triangle \( ABC \) are in the ratio \( 1:2:3 \) (See the picture.). From the following ratios of sides select the one that is equal to \( 1:\sqrt3 \).
\( a:b \)
\( b:a\)
\( c:b \)
\( a:c \)
2010015304
Level:
B
Which of the following formulas applies to the given triangle \( ABC \)? (See the picture.)
\( c^2 = a^2+b^2 -2ab\cos\gamma \)
\( c^2 = a^2+b^2 +2ab\cos\gamma \)
\( c^2 = a^2+b^2 -2ab\cos\alpha \)
\( c^2 = a^2+b^2 -2ab\sin\beta \)