Similarity of triangles - examples

See also our trigonometric triangle calculator.

  1. Ruler
    pravitko_1 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.
  2. Tree shadow
    tree2_1 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. Reverse Pythagorean theorem
    pytagors Given are lengths of the sides of the triangles. Decide which one is rectangular: Δ ABC: 73 m, 66 m, 51 m ? Δ DEF: 63 cm, 105 cm, 84 cm ? Δ GHI: 50 dm, 48 dm, 14 dm ? Δ JKL: 31 m, 45 m, 40 m ? Δ MNO: 28 m, 53 m, 45 m ?
  4. Similarity
    similar_triangle Are two right triangles similar to each other if the first one has a acute angle 10° and second one has acute angle 50°?
  5. Railways
    railways Railways climb 5.8 ‰. Calculate the height difference between two points on the railway distant 2389 meters.
  6. See harmonics
    HarmonicMean 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.
  7. Similarity of squares
    squares2_1 The ratio of the similarity of the squares ABCD and KLMN is 2.5. Square KLMN area is greater than area of a square ABCD with side a: ?
  8. Shadow and light
    stin Nine meters height poplar tree has a shadow 16.2 meters long. How long shadow have at the same time Joe if he is 1,4m tall?
  9. Hexagon
    hexagon There is regular hexagon ABCDEF. If area of the triangle ABC is 19, what is area of the hexagon ABCDEF? I do not know how to solve it simply....
  10. Diagonal in rectangle
    q 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.
  11. Similarity
    podobnost 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.
  12. Cosine
    theta Calculate the cosine of the smallest internal angle in a right-angled triangle with cathetus 19 and 4 and with the hypotenuse 19.416.
  13. Climb
    scenic_road Road has climbing 1:23. How big is a angle corresponds to this climbing?
  14. Geodesist
    XY Triangle shaped field (triangle ABC) has side AB = 51 m. path XY is parallel to the side AB which divided triangle ABC into two parts with same area. What will be the length of the path XY? Help please geodesist ...
  15. Climb
    Mazda_RX7_1 On the road sign, which informs the climb is 20%. Car goes 5 km along this road. What is the height difference that car went?
  16. Triangle KLB
    rovnostranny_trojuholnik It is given equilateral triangle ABC. From point L which is the midpoint of the side BC of the triangle it is drwn perpendicular to the side AB. Intersection of perpendicular and the side AB is point K. How many % of the area of the triangle ABC is area o
  17. Trapezoid IV
    lichobeznik2 In a trapezoid ABCD (AB||CD) is |AB| = 15cm |CD| = 7 cm, |AC| = 12 cm, AC is perpendicular to BC. What area has a trapezoid ABCD?
  18. Similarity coefficient
    eqlateral_triangles The ratio of similarity of two equilateral triangles is 3.9 (ie 39:10). The length of the side of smaller triangle is 3 cm. Calculate the perimeter and area of ​​the larger triangle.
  19. Angle in RT
    triangles_10 Determine the size of the smallest internal angle of a right triangle whose sides constitutes sizes consecutive members of arithmetic progressions.
  20. Inclined plane
    naklonena_rovina On the inclined plane with an angle of inclination of 30 ° we will put body (fixed point) with mass 6 kg. Determine the acceleration of the body motion on an inclined plane.

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