Angle + similarity of triangles - practice problems - last page
Number of problems found: 60
- Three
Three points are given: A (-3, 1), B (2, -4), C (3, 3) a) Find the perimeter of triangle ABC. b) Decide what type of triangle the triangle ABC is. c) Find the length of the inscribed circle - Shadow of tree
Miro stands under a tree and watches its shadow and shadow of the tree. Miro is 180 cm tall, and its shade is 1.5 m long. The tree's shadow is three times as long as Miro's shadow. How tall is the tree in meters? - Mirror
How far must Paul place a mirror to see the top of the tower 12 m high? The height of Paul's eyes above the horizontal plane is 160 cm, and Paul is from the tower distance of 20 m. - Mast angles and height
Calculate the height of the mast, whose foot can be seen at a depth angle of 11° and the top at a height angle of 28°. The mast is observed from a position 10 m above the level of the base of the mast.
- Thales
Thales is 1 m from the hole. The eyes are 150 cm above the ground and look into the hole with a diameter of 120 cm, as shown. Calculate the depth of the hole. - Observation 82811
From the 40 m high observation deck, you can see the top of the poplar at a depth angle of 50*10' and the bottom of the poplar at a depth angle of 58*. Calculate the height of the poplar. - Inclined plane
The body stays on an inclined plane and exerts a compressive force of 70N on it. Find the angle between the inclined plane and the horizontal if a gravitational force of 100N acts on the body. - Tree shadow
The tree perpendicular to the horizontal surface has a shadow 8.32 meters long. At the same time, a one-meter rod perpendicular to the horizontal surface has a shadow 64 cm long. How tall is the tree? - The chimney
The chimney casts a shadow 45 meters long. The one-meter-long rod standing perpendicular to the ground has a shadow 90 cm long. Calculate the height of the chimney.
- Area of iso-trap
Find the area of an isosceles trapezoid if the lengths of its bases are 16 cm and 30 cm, and the diagonals are perpendicular to each other. - Ruler
Peter is looking at John over a ruler that keeps at an arm's distance of 60 cm from the eye, and on the ruler, John measured the height of 15 mm. John is 2 meters high. How far from Peter stands John? - Triangles 6647
For triangles ABC and A'B'C': alpha = alpha with a line, beta with line = beta. a) are these triangles identical? Why? b) are these triangles similar? Why? - Hexagon
There is a regular hexagon ABCDEF. If the area of the triangle ABC is 22, what is the area of the hexagon ABCDEF? I do not know how to solve it simply.... - Rectangular trapezoid
The ABCD rectangular trapezoid with the AB and CD bases is divided by the diagonal AC into two equilateral rectangular triangles. The length of the diagonal AC is 62cm. Calculate the trapezium area in cm square and calculate how many different perimeters
- Rhombus
ABCD is a rhombus, ABD is an equilateral triangle, and AC is equal to 4. Find the area of the rhombus. - Hexagon cut pyramid
Calculate the volume of a regular 6-sided cut pyramid if the bottom edge is 30 cm, the top edge is 12 cm, and the side edge length is 41 cm. - Distance of points
A regular quadrilateral pyramid ABCDV is given, in which edge AB = a = 4 cm and height v = 8 cm. Let S be the center of the CV. Find the distance of points A and S. - Trapezium diagonals
It is given trapezium ABCD with bases | AB | = 12 cm, |CD| = 8 cm. Point S is the intersection of the diagonals for which |AS| is 6 cm long. Calculate the length of the full diagonal AC. - Diagonals at right angle
In the trapezoid ABCD, this is given: AB=12cm CD=4cm And diagonals crossed under a right angle. What is the area of this trapezoid ABCD?
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