System of equations + triangle - math problems

  1. Sides of right angled triangle
    triangle_rt1 One leg is 1 m shorter than the hypotenuse, and the second leg is 2 m shorter than the hypotenuse. Find the lengths of all sides of the right-angled triangle.
  2. Faces diagonals
    cuboid_1 If the diagonals of a cuboid are x, y, and z (wall diagonals or three faces) respectively than find the volume of a cuboid. Solve for x=1.2, y=1.7, z=1.45
  3. Two chords
    tetivy Calculate the length of chord AB and perpendicular chord BC to circle if AB is 4 cm from the center of the circle and BC 8 cm from the center of the circle.
  4. Right triangle Alef
    r_triangle The obvod of a right triangle is 84 cm, the hypotenuse is 37 cm long. Determine the lengths of the legs.
  5. Triangle ABC
    triangles_3 Calculate the sides of triangle ABC with area 1404 cm2 and if a: b: c = 12:7:18
  6. Right triangle
    righttriangle Legs of the right triangle are in the ratio a:b = 2:8. The hypotenuse has a length of 87 cm. Calculate the perimeter and area of the triangle.
  7. R triangle
    right_triangle_1 Calculate the area of a right triangle whose longer leg is 6 dm shorter than the hypotenuse and 3 dm longer than the shorter leg.
  8. Medians
    medias_triangle Calculate the sides of a right triangle if the length of the medians to the legs are ta = 21 cm and tb=12 cm.
  9. RT - hypotenuse and altitude
    pravy_trojuholnik Right triangle BTG has hypotenuse g=117 m and altitude to g is 54 m. How long are hypotenuse segments?
  10. Triangle angles
    triangles_2 The angles α, β, γ in triangle ABC are in the ratio 6:2:6. Calculate size of angles.
  11. Circular sector
    vysek_circle I have a circular sector with a length 15 cm with an unknown central angle. It is inscribed by a circle with radius 5 cm. What is the central angle alpha in the circular sector?
  12. Trapezoid
    lichobeznik_3 trapezoid ABCD a = 35 m, b=28 m c = 11 m and d = 14 m. How to calculate its area?
  13. Angles in a triangle
    fun The angles of the triangle ABC make an arithmetic sequence with the largest angle γ=83°. What sizes have other angles in a triangle?
  14. Angles in triangle
    trigonometry The triangle is ratio of the angles β:γ = 6:8. Angle α is 40° greater than β. What are the size of angles of the triangle?
  15. Isosceles triangle
    pomer_triangle The perimeter of an isosceles triangle is 112 cm. The length of the arm to the length of the base is at ratio 5:6. Find the triangle area.
  16. Angles of the triangle
    angles ABC is a triangle. The size of the angles alpha, beta are in a ratio 4: 7. The angle gamma is greater than the angle alpha by a quarter of a straight angle. Determine angles of the triangle ABC.
  17. Angles ratio
    triangles_16 The internal angles of a triangle are in ratio 1:4:5 What kind of triangle is it? (solve internal angles and write down and discuss)
  18. Clouds
    cloud From two points A and B on the horizontal plane was observed forehead cloud above the two points under elevation angle 73°20' and 64°40'. Points A , B are separated by 2830 m. How high is the cloud?
  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. Diagonal 20
    plaza Diagonal pathway for the rectangular town plaza whose length is 20 m longer than the width. if the pathway is 20 m shorter than twice the width. How long should the pathway be?

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