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 α is 47°, find side a. Please round to one decimal.
• Triangle SAS
  Calculate the triangle area and perimeter if the two sides are 46 m and 33 m long and angle them clamped is 170 °.
• Scalene triangle
  Solve the triangle: A = 50°, b = 13, c = 6
• Greatest angle
  Calculate the greatest triangle angle with sides 124, 323, 302.
• Side c
  In △ABC a=1, b=6 and ∠C=110°. Calculate the length of the side c.
• The aspect ratio
  The aspect ratio of the rectangular triangle is 13:12:5. Calculate the internal angles of the triangle.
• Cosine - legs
  Using the law of cosines, find the measurement of leg b if the givens are β=20°, a=10, and c=15.
• Calculate 2
  Calculate the largest angle of the triangle whose sides are 5.2cm, 3.6cm, and 2.1cm
• 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?
• 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).
• Triangle and its heights
  Calculate the length of the sides of the triangle ABC if v_a=13 cm, v_b=15 cm and side b are 5 cm shorter than side a.
• Medians of isosceles triangle
  The isosceles triangle has a base ABC |AB| = 16 cm and a 10 cm long arm. What is the length of the medians?
• SAS triangle
  The triangle has two sides, long 7 and 19, and includes angle 47°24'. Calculate the area of this triangle.
• 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.
• Diagonals
  Calculate the length of the rhombus's diagonals if its side is long 21 and one of its internal angles is 10°.
• 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.

more triangle problems »

Also, take a look 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.