Geometry of the triangle

Mathematics beauty

Geometry of the triangle eTwinning project 2020-2021

Coord. teacher:

Cojocari Ludmila

Alina Stefania Lazar, Elena Georgiana Citu Aliona Beșliu, Sophie Dupont Burcu Ünal Solmaz, Tuğba Varol

Nr.

Task problem

The Team who draw Drawing/solution

The image shows a tower and a stick placed perpendicular to the ground. The length of the stick is 2 meters, the shadow left by the stick is one meter long, and the one left by the tower is 7m. What is the height of the tower?

Republic of Moldova

2.

A tree has a shade of 8.4 m., While a person with a height of 1.8 m has a shade of 0.7 m.

What is the height of the tree?

Moldova Team 2

3.

The figure shows two balls A and B on a pool table. Ball A must hit ball B after it touches the edge of the table in C. Determine A1C, knowing that AA1 = 45 cm, A1B1 = 15 cm

Moldova Team 3

1.

The team who solve Solutions Romania Team 1 Turkey Team 2

România Team 2

France Team 1

Moldova Team 1

4.

Andrei sees the top of a mast V reflected in a mirror X which is located on the line determined by the position of P and the base of the mast B. Find the height BV of the mast, knowing that PX = 1.22 m, BX = 7.32 m, AP = 1.82 m

Moldova Team 4

Moldova Team 3

5.

A pine tree grew between two buildings A and B. Determine the height of the pine tree, knowing that its top V belongs to the lines MR and NQ, MQ = 60 m, and NR = 40 m.

Moldova Team 1

Turkey Team 2

6.

A ladder, which is supported by a wall, reaches a cube-shaped box with a side of 1 m. Find out how high the ladder reaches, knowing that the distance from its foot to the wall is 1.5 m.

Moldova Team 2

Turkey Team 1

7.

Around a castle, with a height of 12 m, a wall located 20 m from the castle must be built.

What must be the height of the wall so that a man 2 m tall, standing beyond the wall, at a distance of less than 5 m from him, cannot see the building?

Moldova Team 3

Turkey Team 1

8.

To get from point A to point B you must avoid walking through a pond. To avoid the pond, you must 34m south and 41 meters east. To the nearest meter, how many meters would be saved if it were possible to walk through the pond?

French Team 1

Moldova Team 1

9.

Find the height of the mountain in the picture.

Moldova Team 3

Moldova Team 2

10.

In the drawing, we can see the statue of liberty and a block.

Find the height of the statue knowing that its shadow is equal to 186 m, the height of the block is equal to 58 m, and the shadow of the block is 116 m.

Team 1, Moldova

Romania, Team 1

11.

In the triangle ABC given above, [AB] ⊥ [BC], [AD] ⊥ [DE], | AD | = 6 cm, | DE | = 8 cm, | BD | = 9 cm, | BC | = 20 cm, how many cm2 is the area of the painted area?

Turkey, Team 1

French team

12.

How many cm2 is the area of the painted area?

Turkey, Team 2

Romania, team 1

13.

In triangle ABC above, [BD] and [CD] are bisectors.

Turkey, Team 3

Moldova, Team 2

Turkey, Team 1

France, team 2

m ^ h BD \ C = 110c, how many degrees is the angle A?

14.

How many cm is the shadow of the pencil above?

15.

The triangle with the side lengths of 8cm, 10cm and 12cm is folded from the middle point of the sides with 10cm and 12cm lengths, as shown in the figure, to create a trapezoid. How many cm is the circumference of the obtained trapezoid?

Turkey, Team 2

Moldova, Team 1

16.

In the drawing we see Buckingham Palace and a lantern. The height of the lantern is 2 meters, its shadow is 4 m, and dhe height of the palace is equal to 24m. Find out the length of the palace shadow.

Moldova, Team 3

Moldova, team 1

17.

A pole is anchored by means of two cables AB and AC (B, D, C are collinear) which form an angle of 90 degrees between them. If BD = 18 cm, CD = 50 m, find the height of the pole.

Moldova, Team 2

Moldova, team 1

18.

A shelf attached to a wall is schematically represented in the figure by the segment AD. For support, the shelf is "anchored" with two wires AB and AC, perpendicular to each other. If BD = 18 cm and CD = 32 cm, find out:

Moldova, team 1

Moldova, team 2

a) shelf length; b) the length of the wire AB and the wire AC.