Triangle calculator SAS

This calculator calculate the missing information of a triangle when given the SAS (Side-Angle-Side) 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 γ between them, you can use the Law of Cosines to find the length of the third side (c) as:

c² = a² + b² - 2ab * cos γ

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

a/sin α = b/sin β = c/sin γ = 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
• Greatest angle
  Calculate the greatest triangle angle with sides 124, 323, 302.

• 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.
• 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.
• Isosceles triangle and cosine
  Using the cosine theorem, prove that in an isosceles triangle ABC with base AB, c=2a cos α.
• Vector sum
  The magnitude of the vector u is 2 and the magnitude of the vector v is 11. The angle between vectors is 64°. What is the magnitude of the vector u + v?

• 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.
• 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).
• ABCD
  AC= 40cm , angle DAB=38 , angle DCB=58 , angle DBC=90 , DB is perpendicular on AC , find BD and AD
• 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.

• Two forces 3
  Two forces with magnitudes 8 Newtons and 15 Newtons act at a point. Find the angle between the forces if the resultant force is 17 Newtons.
• 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.
• Cosine - legs
  Using the law of cosines, find the measurement of leg b if the givens are β=20°, a=10, and c=15.

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.