Equilateral triangle

A square is inscribed into an equilateral triangle with a side of 10 cm. Calculate the length of the square side.

Correct result:

b =  4.641 cm

Solution:

a=10 cm h=a2(a/2)2=102(10/2)2=5 3 cm8.6603 cm  tan(60)=b/x a=2x+b  tan(60) (ab)/2=b  a/2 tan(60)=b(1+tan(60)/2)   b=a2 tan601+tan60/2=tanπ/3=4.641=9719π/6579=4.641 cm



We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you!






Showing 0 comments:
avatar




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

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

Next similar math problems:

  • Right triangle eq2
    rt_triangle_1 Find the lengths of the sides and the angles in the right triangle. Given area S = 210 and perimeter o = 70.
  • Cone side
    kuzel3 Calculate the volume and area of the cone whose height is 10 cm and the axial section of the cone has an angle of 30 degrees between height and the cone side.
  • Nonagon
    9gon Calculate the area and perimeter of a regular nonagon if its radius of inscribed circle is r = 10cm
  • 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.
  • Traffic sign
    cyklo2 There is a traffic sign for climbing on the road with an angle of 7%. Calculate at what angle the road rises (falls).
  • Pentagon
    5gon Calculate the length of side, circumference and area of a regular pentagon, which is inscribed in a circle with radius r = 6 cm.
  • Pyramid 8
    ihlan Calculate the volume and the surface area of a regular quadrangular pyramid with the base side 9 cm and side wall with the base has an angle 75°.
  • Four sided prism
    hranol4sreg Calculate the volume and surface area of a regular quadrangular prism whose height is 28.6cm and the body diagonal forms a 50 degree angle with the base plane.
  • An equilateral
    rs_triangle2 An equilateral triangle is inscribed in a square of side 1 unit long so that it has one common vertex with the square. What is the area of the inscribed triangle?
  • 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.
  • The tower
    veza_huly The observer sees the base of the tower 96 meters high at a depth of 30 degrees and 10 minutes and the top of the tower at a depth of 20 degrees and 50 minutes. How high is the observer above the horizontal plane on which the tower stands?
  • 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.
  • Sphere in cone
    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
  • Railway embankment
    rr_lichobeznik The section of the railway embankment 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.
  • Rectangular trapezoid
    right-trapezium-figure The ABCD rectangular trapezoid with the AB and CD bases is divided by the diagonal AC into two equilateral rectangular triangles. The length of the diagonal AC is 62cm. Calculate trapezium area in cm square and calculate how many differs perimeters of the
  • Vertical rod
    shadow 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.
  • Diagonals of pentagon
    5gon_diagonal Calculate the diagonal length of the regular pentagon: a) inscribed in a circle of radius 12dm; b) a circumscribed circle with a radius of 12dm.