Triangle calculator SAS

To calculate the missing information of a triangle when given the SAS theorem, you can use the known side lengths and angles to find the remaining side length and angles using trigonometry or geometry.

If you know the lengths of two sides (a and b) and the angle (C) between them, you can use the Law of Cosines to find the length of the third side (c) as:

c² = a² + b² - 2ab * cos(C)

Once you have the length of the third side, you can use the Law of Sines to find the remaining angles (A and B) as:

a/sin(A) = b/sin(B) = c/sin(C) = 2R

Where R is the circumradius of the triangle

You can also use the given side lengths and angles to find the area of the triangle using Heron's formula or using trigonometric functions like Sin or Cos.

It's important to note that you need to have the measures of two sides and the angle between them to use this theorem. If you have only two sides or one side and one angle, it would not be possible to determine the triangle completely.

If you know two sides and one adjacent angle, use the SSA calculator.

Triangle SAS theorem math problems:

• SAS calculation
  Given the triangle ABC, if side b is 31 ft., side c is 22 ft., and angle A is 47°, find side a. Please round to one decimal.
• Triangle SAS
  Calculate the triangle area and perimeter if the two sides are 105 dm and 68 dm long and angle them clamped is 50 °.
• Scalene triangle
  Solve the triangle: A = 50°, b = 13, c = 6
• Vector sum
  The magnitude of the vector u is 12 and the magnitude of the vector v is 10. The angle between vectors is 61°. What is the magnitude of the vector u + v?

• Greatest angle
  Calculate the greatest triangle angle with sides 124, 323, 302.
• Diagonals
  Calculate the length of the rhombus's diagonals if its side is long 5 and one of its internal angles is 80°.
• The aspect ratio
  The aspect ratio of the rectangular triangle is 13:12:5. Calculate the internal angles of the triangle.
• Side c
  In △ABC a=1, b=6 and ∠C=110°. Calculate the length of the side c.
• The angle of view
  Determine the angle of view at which the observer sees a rod 16 m long when it is 18 m from one end and 27 m from the other.

• A rhombus
  A rhombus has sides of the length of 10 cm, and the angle between two adjacent sides is 76 degrees. Find the length of the longer diagonal of the rhombus.
• Calculate 2
  Calculate the largest angle of the triangle whose sides are 5.2cm, 3.6cm, and 2.1cm
• Triangle and its heights
  Calculate the length of the sides of the triangle ABC if v_a=5 cm, v_b=7 cm and side b are 5 cm shorter than side a.
• ABCD
  AC= 40cm , angle DAB=38 , angle DCB=58 , angle DBC=90 , DB is perpendicular on AC , find BD and AD
• Angles by cosine law
  Calculate the size of the angles of the triangle ABC if it is given by: a = 3 cm; b = 5 cm; c = 7 cm (use the sine and cosine theorem).

• Cosine
  Cosine and sine theorem: Calculate all missing values from triangle ABC. c = 2.9 cm; β = 28°; γ = 14° α =? °; a =? cm; b =? cm
• Four sides of trapezoid
  In the trapezoid ABCD is |AB| = 73.6 mm; |BC| = 57 mm; |CD| = 60 mm; |AD| = 58.6 mm. Calculate the size of its interior angles.
• Isosceles 83157
  Using the cosine theorem, prove that in an isosceles triangle ABC with base AB, c=2a cos α.

more triangle problems »

Look also at our friend's collection of math problems and questions:

• triangle
• right triangle
• Heron's formula
• The Law of Sines
• The Law of Cosines
• Pythagorean theorem
• triangle inequality
• similarity of triangles
• The right triangle altitude theorem

See triangle basics on Wikipedia or more details on solving triangles.