Ratio + right triangle - math problems

Number of problems found: 130

  • Calculate
    Calculate the height of a tree that casts a shadow 22 m long, if you know that at the same time a pillar 2 m high casts a shadow 3 meters long.
  • Sides in ratio
    The sides of the triangle are in a ratio of 2: 8: 5. Find the dimensions of the remaining sides if the longest side is 32 cm.
  • Construct 8
    Construct an analytical geometry problem where it is asked to find the vertices of a triangle ABC: the vertices of this triangle must be the points A (1,7) B (-5,1) C (5, -11). the said problem should be used the concepts of: distance from a point to a li
  • Centre of the hypotenuse
    For the interior angles of the triangle ABC, alpha beta and gamma are in a ratio of 1: 2: 3. The longest side of the AB triangle is 30 cm long. Calculate the perimeter of the triangle CBS if S is the center of the side AB.
  • Center of gravity and median
    In the isosceles triangle ABC, the center of gravity T is 2 cm from the base AB. The median parallel to the AB side measures 4 cm. What is the area of the ABC triangle?
  • MIT 1869
    You know the length of hypotenuse parts 9 and 16, at which the hypotenuse of a right triangle is divided by a perpendicular running from its opposite vertex. The task is to find the lengths of the sides of the triangle and the length of the line x. This a
  • Calculate
    Calculate the area of triangle ABC, if given by alpha = 49°, beta = 31°, and the height on the c side is 9cm.
  • The truncated
    The truncated rotating cone has bases with radii r1 = 8 cm, r2 = 4 cm and height v = 5 cm. What is the volume of the cone from which the truncated cone originated?
  • Two cables
    On a flat plain, 2 columns are erected vertically upwards. One is 7 m high and the other 4 m. Cables are stretched between the top of one column and the foot of the other column. At what height will the cables cross? Assume that the cables do not sag.
  • Ratio in trapezium
    The height v and the base a, c in the trapezoid ABCD are in the ratio 1: 6: 3, its content S = 324 square cm. Peak angle B = 35 degrees. Determine the perimeter of the trapezoid
  • Ratio of triangles areas
    In an equilateral triangle ABC, the point T is its centre of gravity, the point R is the image of the point T in axial symmetry, along the line AB, and the point N is the image of the point T in axial symmetry along the line BC. Find the ratio of the area
  • Railway embankment
    The railway embankment section is an isosceles trapezoid, the sizes of the bases of which are in the ratio 5: 3. The arms have a length of 5 m, and the height of the embankment is 4.8 m. Calculates the size of the embankment section area.
  • A cliff
    A line from the top of a cliff to the ground passes just over the top of a pole 5 ft high and meets the ground at a point 8 ft from the base of the pole. If the point is 93 ft from the base of the​ cliff, how high is the​ cliff?
  • Vertical rod
    The vertical one-meter-long rod casts a shadow 150 cm long. Calculate the height of a column whose shadow is 36 m long at the same time.
  • The straight
    The straight path rises by 72 cm every 3 m of its length. How many meters will it climb to 350 m?
  • Sphere in cone
    A sphere is inscribed in the cone (the intersection of their boundaries consists of a circle and one point). The ratio of the surface of the ball and the contents of the base is 4: 3. A plane passing through the axis of a cone cuts the cone in an isoscele
  • Chimney and tree
    Calculate the height of the factory chimney, which casts a shadow 6.5 m long in the afternoon. At the same time, a 6 m high tree standing near it casts a shadow 25 dm long.
  • Similar triangles
    The triangles ABC and XYZ are similar. Find the missing lengths of the sides of the triangles. a) a = 5 cm b = 8 cm x = 7.5 cm z = 9 cm b) a = 9 cm c = 12 cm y = 10 cm z = 8 cm c) b = 4 cm c = 8 cm x = 4.5 cm z = 6 cm
  • Powerplant chimney
    From the building window at the height of 7.5 m, we can see the top of the factory chimney at an altitude angle of 76° 30 ′. We can see the chimney base from the same place at a depth angle of 5° 50 ′. How tall is the chimney?
  • Similarity coefficient
    In the triangle TMA the length of the sides is t = 5cm, m = 3.5cm, a = 6.2cm. Another similar triangle has side lengths of 6.65 cm, 11.78 cm, 9.5 cm. Determine the similarity coefficient of these triangles and assign similar sides to each other.

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