Right triangle - ratio

The lengths of the legs of the right triangle ABC are in ratio b = 2: 3. The hypotenuse is 10 cm long. Calculate the lengths of the legs of that triangle.

Correct result:

a =  5.547 cm
b =  8.321 cm


a:b=2:3 b=3/2 a c=10 cm   c2=a2+b2 c2=a2+(3/2a)2 c2=a2+(3/2)2 a2 a=c21+(3/2)2=1021+(3/2)2=5.547 cma:b=2:3 \ \\ b=3/2 \cdot \ a \ \\ c=10 \ \text{cm} \ \\ \ \\ \ \\ c^2=a^2+b^2 \ \\ c^2=a^2+(3/2a)^2 \ \\ c^2=a^2+(3/2)^2 \cdot \ a^2 \ \\ a=\sqrt{ \dfrac{ c^2 }{ 1+(3/2)^2 } }=\sqrt{ \dfrac{ 10^2 }{ 1+(3/2)^2 } }=5.547 \ \text{cm}
b=3/2 a=3/2 5.547=8.321 cmb=3/2 \cdot \ a=3/2 \cdot \ 5.547=8.321 \ \text{cm}

Try calculation via our triangle calculator.

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Please write to us with your comment on the math problem or ask something. Thank you for helping each other - students, teachers, parents, and problem authors.

Showing 0 comments:

Tips to related online calculators
Check out our ratio calculator.
Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation?
Pythagorean theorem is the base for the right triangle calculator.
See also our trigonometric triangle calculator.

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

Next similar math problems:

  • Sailboat
    Plachetnice The 20 m long sailboat has an 8 m high mast in the middle of the deck. The top of the mast is fixed to the bow and stern with a steel cable. Determine how much cable is needed to secure the mast and what angle the cable will make with the ship's deck.
  • Hexagonal pyramid
    hexa_pyramid Find the volume of a regular hexagonal pyramid, the base edge of which is 12 cm long and the side edge 20 cm.
  • An observer
    tower An observer standing west of the tower sees its top at an altitude angle of 45 degrees. After moving 50 meters to the south, he sees its top at an altitude angle of 30 degrees. How tall is the tower?
  • Chord of triangle
    triangle_1212 If the whole chord of the triangle is 14.4 cm long, how do you calculate the shorter and longer part?
  • Pentadecagon
    220px-Regular_polygon_15_annotated.svg Calculate the content of a regular 15-sides polygon inscribed in a circle with radius r = 4. Express the result to two decimal places.
  • Dodecagon
    clocks Calculate the size of the smaller of the angles determined by lines A1 A4 and A2 A10 in the regular dodecagon A1A2A3. .. A12. Express the result in degrees.
  • Coils of transformer
    voltemeter The primary coil of the transformer has 1100 turns and is connected to a voltage of 220V. How many turns does the secondary coil have when the voltage on it is 55 V? Determine the transformation ratio and decide what kind of transformation is it.
  • Coils of transformer
    transformator The primary coil of the transformer has 400 turns, a current of 1.5 A passes through it and is connected to a voltage of 220 V. For the secondary coil, find the voltage, current, and a number of turns if the transformation ratio k = 0.1.
  • Twice of radius
    gule How many times does the surface of a sphere decrease if we reduce its radius twice?
  • Square and circles
    squares_cut_circles The square in the picture has a side length of a = 20 cm. Circular arcs have centers at the vertices of the square. Calculate the areas of the colored unit. Express area using side a.
  • Lookout tower
    tower How high is the lookout tower? If each step was 3 cm lower, there would be 60 more of them on the lookout tower. If it was 3 cm higher again, it would be 40 less than it is now.
  • Shell area cy
    valec The cylinder has a shell content of 300 cm square, while the height of the cylinder is 12 cm. Calculate the volume of this cylinder.
  • The cylinder
    valec2_1 The cylinder has a surface area of 300 square meters, while the height of the cylinder is 12 m. Calculate the volume of this cylinder.
  • In the
    rectangle_1 In the rectangle ABCD, the distance of its center from the line AB is 3 cm greater than from the line BC. The circumference of the rectangle is 52 cm. Calculate the contents of the rectangle. Express the result in cm2.
  • 1 page
    books 1 page is torn from the book. The sum of the page numbers of all the remaining pages is 15,000. What numbers did the pages have on the page that was torn from the book?
  • Cylinder container
    valec2 The cylindrical container with a diameter of 1.8 m contains 2,000 liters of water. How high does the water reach?
  • On a line
    linearna On a line p : 3 x - 4 y - 3 = 0, determine the point C equidistant from points A[4, 4] and B[7, 1].