# Similarity of triangles - examples - page 2

1. Cosine
Calculate the cosine of the smallest internal angle in a right-angled triangle with cathetus 3 and 8 and with the hypotenuse 8.544.
Tree perpendicular to the horizontal surface has a shadow 8.32 meters long. At the same time meter rod perpendicular to the horizontal surface has shadow 64 cm long. How tall is tree?
3. Diagonal in rectangle
In that rectangle ABCD is the center of BC point E and point F is center of CD. Prove that the lines AE and AF divide diagonal BD into three equal parts.
4. See harmonics
It is true that the size of the central segment of any trapezoid is the harmonic mean size of its bases? Prove it. Central segment crosses the intersection of the diagonals and is parallel to the bases.
5. Angle in RT
Determine the size of the smallest internal angle of a right triangle whose sides constitutes sizes consecutive members of arithmetic progressions.
6. Garage
There are two laths in the garage opposite one another: one 2 meters long and the second 3 meters long. They fall against each other and stay against the opposite walls of the garage and both laths cross 70 cm above the garage floor. How wide is the garag
7. Area and two angles
Calculate the size of all sides and internal angles of a triangle ABC, if it is given by area S = 501.9; and two internal angles α = 15°28' and β = 45°.
8. Rhombus
ABCD is a rhombus, ABD is an equilateral triangle and AC is equal to 4. Find the area of the rhombus.
9. Traffic laws
Under traffic regulations, car lights can illuminate the road up to a maximum of 30 m. To check the reach of the dipped-beam lights of their car, Peter stopped car at 1.5 m from the wall. The dipped-beam headlights are 60 cm high. At what height on the wa
The shadow of the tree is 16 meters long. Shadow of two meters high tourist sign beside standing is 3.2 meters long. What height has tree (in meters)?
11. MO Z9–I–2 - 2017
In the VODY trapezoid, VO is a longer base and the diagonal intersection K divides the VD line in a 3:2 ratio. The area of the KOV triangle is 13.5 cm2. Find the area of the entire trapezoid.
12. Similarity
ABC is a triangle wherein a = 4 cm, b = 6 cm, c = 8 cm. Is it similar to the triangle DEF: d = 3 cm, e = 4.5 cm, f = 6 cm? If so, determine the ratio of similarity.
13. Isosceles trapezoid
In an isosceles trapezoid KLMN intersection of the diagonals is marked by the letter S. Calculate the area of trapezoid if /KS/: /SM/ = 2:1 and a triangle KSN is 14 cm2.
14. Sides od triangle
Sides of the triangle ABC has length 4 cm, 5 cm and 7 cm. Construct triangle A'B'C' that are similar to triangle ABC which has a circumference of 12 cm.
15. V-belt
Calculate a length of the V-belt when the diameter of the pulleys is: D1 = 600 mm D2 = 120 mm d = 480 mm
16. 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 distant 20 m.
17. Sides ratio
Calculate the circumference of a triangle with area 84 cm2 if a:b:c = 10:17:21
18. Ruler
How far from Peter stands 2m hight John? Petr is looking to John over ruler that keeps at arm's distant 60 cm from the eye and on the ruler John measured the height of 15 mm.
19. Equilateral triangle ABC
In the equilateral triangle ABC, K is the center of the AB side, the L point lies on one-third of the BC side near the point C, and the point M lies in the one-third of the side of the AC side closer to the point A. Find what part of the ABC triangle conta
20. Hexagon cut pyramid
Calculate the volume of a regular 6-sided cut pyramid if the bottom edge is 30 cm, the top edge us 12 cm, and the side edge length is 41 cm.

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