Three altitudes

A triangle with altitudes 4; 5, and 6 cm is given. Calculate the lengths of all medians and all sides in a triangle.

Correct answer:

a =  7.5236 cm
b =  6.0189 cm
c =  5.0157 cm
t1 =  4.0671 cm
t2 =  5.6413 cm
t3 =  6.3345 cm

Step-by-step explanation:

v1=4 cm v2=5 cm v3=6 cm  h=1/v1+1/v2+1/v32=1/4+1/5+1/62=371200.3083 t=h (h1/v1) (h1/v2) (h1/v3)=0.3083 (0.30831/4) (0.30831/5) (0.30831/6)0.0003  s=4 t=4 0.00030.0665 S=1s=10.066515.0472 cm2  S=a v12  a=2 S/v1=2 15.0472/4=7.5236 cm

Try calculation via our triangle calculator.

b=2 Sv2=2 15.04725=6.0189 cm
c=2 Sv3=2 15.04726=5.0157 cm
t1=2 b2+2 c2a22=2 6.01892+2 5.015727.523622=4.0671 cm
t2=2 a2+2 c2b22=2 7.52362+2 5.015726.018922=5.6413 cm
t3=2 a2+2 b2c22=2 7.52362+2 6.018925.015722=6.3345 cm



Did you find an error or inaccuracy? Feel free to write us. Thank you!






avatar




Tips to related online calculators
Looking for calculator of harmonic mean?
Looking for a statistical calculator?
Do you have a linear equation or system of equations and looking for its solution? Or do you have a quadratic equation?
Do you want to convert length units?
See also our trigonometric triangle calculator.
Pythagorean theorem is the base for the right triangle calculator.

 
We encourage you to watch this tutorial video on this math problem: video1   video2

Related math problems and questions:

  • Medians in right triangle
    triangle_rt_taznice It is given a right triangle, angle C is 90 degrees. I know it medians t1 = 8 cm and median t2 = 12 cm. .. How to calculate the length of the sides?
  • Medians in RT
    right_triangle The rectangular triangle ABC has a length of 10 cm and 24 cm. Points P, Q, R are the centers of the sides of this triangle. The perimeter of the PQR triangle is:
  • Medians and sides
    taznice3 Triangle ABC in the plane Oxy; are the coordinates of the points: A = 2.7 B = -4.3 C-6-1 Try calculate lengths of all medians and all sides.
  • Rhombus
    kosostvorec The rhombus has diagonal lengths of 4.2cm and 3.4cm. Calculate the length of the sides of the rhombus and its height
  • Rectangle 3-4-5
    diagonal_rectangle The sides of the rectangle are in a ratio of 3:4. The length of the rectangle diagonal is 20 cm. Calculate the content of the rectangle.
  • Tetrahedral pyramid
    jehlan A regular tetrahedral pyramid is given. Base edge length a = 6.5 cm, side edge s = 7.5 cm. Calculate the volume and the area of its face (side area).
  • Diamond diagonals
    kosostvorec Calculate the diamond's diagonal lengths if its content is 156 cm2 and the side length is 13 cm.
  • Similar triangles
    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
  • Triangle in a square
    stvorec In a square ABCD with side a = 6 cm, point E is the center of side AB, and point F is the center of side BC. Calculate the size of all angles of the triangle DEF and the lengths of its sides.
  • Diagonal
    trapezium_right The rectangular ABCD trapeze, whose AD arm is perpendicular to the AB and CD bases, has an area of 15 cm square. Bases have lengths AB = 6cm, CD = 4cm. Calculate the length of the AC diagonal.
  • Isosceles trapezoid
    lichobeznik Calculate the content of an isosceles trapezoid whose bases are at ratio 5:3, the arm is 6cm long and it is 4cm high.
  • Frustrum - volume, area
    frustum-of-a-right-circular-cone Calculate the surface and volume of the truncated cone, the radius of the smaller figure is 4 cm, the height of the cone is 4 cm and the side of the truncated cone is 5 cm.
  • Side lengths
    triangles In the triangle ABC, the height to the side a is 6cm. The height to side b is equal to 9 cm. Side "a" is 4 cm longer than side "b". Calculate the side lengths a, b.
  • Ratio of sides
    trojuholnik The triangle has a circumference of 21 cm, and the length of its sides is in a ratio of 6: 5: 3. Find the length of the longest side of the triangle in cm.
  • Euclid theorems
    euklidova_veta_trojuhelnik_nakres Calculate the sides of a right triangle if leg a = 6 cm, and a section of the hypotenuse, which is located adjacent to the second leg b is 5cm.
  • Isosceles trapezium
    rr_lichobeznik Calculate the area of an isosceles trapezium ABCD if a = 10cm, b = 5cm, c = 4cm.
  • Harmonic mean
    means_math If x, y, z form a harmonic progression, then y is the harmonic mean of x and z. Find the harmonic mean of the numbers 6 and 5.