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
• Cosine - legs
  Using the law of cosines, find the measurement of leg b if the givens are β=20°, a=10, and c=15.
• Isosceles triangle and cosine
  Using the cosine theorem, prove that in an isosceles triangle ABC with base AB, c=2a cos α.
• 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.
• 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.

• Parallelogram 65954
  In the parallelogram ABCD AB = 8, BC = 5, BD = 7. Calculate the magnitude of the angle α = ∠DAB (in degrees).
• Rhombus 36
  Rhombus ABCD with side 8 cm long has diagonal BD 11.3 cm long. Find angle DAB.
• Sides ratio and angles
  In triangle ABC, you know the ratio of side lengths a:b:c=3:4:6. Calculate the angle sizes of triangle ABC.
• A triangle 7
  A triangle lot has the dimensions a=15m, b=10m, and c=20m. What is the measure of the angle between the sides of b and c?
• Two triangles SSA
  We can form two triangles with the given information. Use the Law of Sines to solve the triangles. A = 59°, a = 13, b = 14
• Observation angle
  At what angle of view does an object 70 m long appear to the observer, 50 m away from one end and 80 m from the other end?
• Calculate 82578
  The vertices of triangle ABC are: A[1, 2, -3], B[0, 1, 2], C[2, 1, 1]. Calculate the lengths of sides AB, AC and the angle at vertex A.
• Side c
  In △ABC a=1, b=6 and ∠C=110°. Calculate the length of the side c.

• Three 235
  Three houses form a triangular shape. House A is 50 feet from house C and house B is 60 feet from house C. The measure is angle ABC is 80 degrees. Draw a picture and find the distance between A and B.
• Greatest angle
  Calculate the greatest triangle angle with sides 124, 323, 302.

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.