2010015205
Level:
A
The measures of two interior angles of a triangle are \( 61^{\circ}20' \) and \( 28^{\circ} \). What is the measure of the third interior angle?
\( 90^{\circ}40' \)
\( 33^{\circ}20' \)
\( 145^{\circ}20' \)
\( 147^{\circ}40' \)
Triangles
2010015208
Level:
A
In the triangle \( ABC \), \( \alpha=80^{\circ} \) and \( \gamma=30^{\circ} \) (see the picture). Determine the measure of the angle between the altitude to the side \( AC \) and the altitude to the side \( AB \).
\( 80^{\circ} \)
\(30^{\circ}\)
\(70^{\circ}\)
\(100^{\circ}\)
2010015209
Level:
A
What is the measure of the angle \( \alpha \)? (See the picture.)
\( 72^{\circ} \)
\(44^{\circ}\)
\(88^{\circ}\)
\(108^{\circ}\)
9000121701
Level:
A
Consider a triangle \(ABC\) with
sides of the lengths \(3\, \mathrm{cm}\),
\(4\, \mathrm{cm}\) and
\(4\, \mathrm{cm}\). Identify the type
of the triangle \(ABC\).
isosceles
equilateral
right
obtuse
9000121702
Level:
A
Consider a triangle \(ABC\) with
sides of the lengths \(3\, \mathrm{cm}\),
\(4\, \mathrm{cm}\) and
\(5\, \mathrm{cm}\). Identify the type
of the triangle \(ABC\).
right
isosceles
equilateral
obtuse
9000121703
Level:
A
Consider a triangle \(ABC\) with
sides of the lengths \(4\, \mathrm{cm}\),
\(4\, \mathrm{cm}\) and
\(4\, \mathrm{cm}\). Identify the type
of the triangle \(ABC\).
equilateral
isosceles
right
obtuse
9000121704
Level:
A
Find the measure of the angle \(CAB\)
in an isosceles triangle \(ABC\)
with the interior angle \( BCA\)
of the measure \(120^{\circ }\).
\(30^{\circ }\)
\(60^{\circ }\)
\(15^{\circ }\)
\(45^{\circ }\)
9000121705
Level:
A
Consider an isosceles triangle \(ABC\) with sides \(AC\) and \(BC\) of equal length. The measure of the angle \( BAC\) is \(40^{\circ }\). \(X\) is the point of intersection between the line $AB$ and the line through the vertex \(C\) perpendicular to it. Find the measure of the angle \( BCX\).
\(50^{\circ }\)
\(80^{\circ }\)
\(100^{\circ }\)
\(40^{\circ }\)
1003021803
Level:
B
The ladder is leaning against the wall of a house. Its length is \( 6 \) meters. How high does the ladder reach if the angle between it and the wall is \( 30^{\circ} \)? (See the picture.)
\( 3\sqrt3\,\mathrm{m} \)
\( 3\,\mathrm{m} \)
\( 6\,\mathrm{m} \)
\( \frac{\sqrt3}2\,\mathrm{m} \)
1003021805
Level:
B
In a triangle with interior angles \( 30^{\circ} \), \( 60^{\circ} \) and \( 90^{\circ} \), the longest side is \( 10\,\mathrm{cm} \) long. Find the length of its shortest side.
\( 5\,\mathrm{cm} \)
\( 5\sqrt3\,\mathrm{cm} \)
\( 3\,\mathrm{cm} \)
\( 8\,\mathrm{cm} \)