Triangle calculator ASA

The ASA (Angle-Side-Angle) theorem is a statement in geometry that states that if two angles of a triangle are equal to two angles of another triangle and the side between those angles is common in both triangles, then the triangles are congruent.

To calculate the missing information of a triangle when given the ASA theorem, you can use the known angles and side lengths to find the remaining side lengths and angles.

If you know the measures of two angles (A and C) and the length of one side (b) between them, you can use the Law of Cosines to find the length of the remaining sides (a and c) as:

a² = b² + c² - 2bc * cos(A)

c² = a² + b² - 2ab * cos(C)

Once you have the length of the two remaining sides, you can use the Law of Sines to find the measure of the angle (B) that is not given 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 angles and side length 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 angles and one side to use this theorem. If you have only one angle and one side, it would not be possible to determine the triangle completely.

If you know one side, adjacent, and opposite angles use the AAS calculator.

Triangle ASA theorem math problems:

• The aspect ratio
  The aspect ratio of the rectangular triangle is 13:12:5. Calculate the internal angles of the triangle.
• Sine theorem 2
  From the sine theorem, find the ratio of the sides of a triangle whose angles are 30°, 60°, and 90°.
• 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
• 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?

• 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
• 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
• 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 75
  Triangle ABC has angle C bisected and intersected AB at D. Angle A measures 20 degrees, and angle B measures 40 degrees. The question is to determine AB-AC if length AD=1.

• Parallelogram 6049
  Calculate the area of the parallelogram if a = 57cm, the diagonal u = 66cm, and the angle against the diagonal is beta β = 57° 43'
• Calculate 4422
  Calculate the perimeter of the triangle ABC if a = 12 cm, the angle beta is 38 degrees, and the gamma is 92 degrees.
• Largest angle of the triangle
  Calculate the largest angle of the triangle whose sides have the sizes: 2a, 3/2a, 3a
• Mast shadow
  The mast has a 13 m long shadow on a slope rising from the mast foot toward the shadow angle at an angle of 15°. Determine the height of the mast if the sun above the horizon is at an angle of 33°. Use the law of sines.
• 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.

• Children playground
  The playground has a trapezoid shape, and the parallel sides have a length of 36 m and 21 m. The remaining two sides are 14 m long and 16 m long. Find the size of the inner trapezoid angles.
• Viewing angle
  The observer sees a straight fence 60 m long at a viewing angle of 30°. It is 102 m away from one end of the enclosure. How far is the observer from the other end of the enclosure?
• Rhomboid
  The rhomboid sides' dimensions are a= |AB|=5cm, b = |BC|=6 cm, and the angle's size at vertex A is 60°. What is the length of the diagonal AC?

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.