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 α

c² = a² + b² - 2ab * cos γ

Once you have the length of the two remaining sides, you can use the Law of Sines to find the measure of the angle β that is not given 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 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:

• Perimeter - ASA theorem
  Calculate the perimeter of the triangle ABC if a = 12 cm, the angle beta is 38 degrees, and the gamma is 92 degrees.
• 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.
• 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.
• 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
• 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.
• Hypotenuse and center
  Point S is the center of the hypotenuse AB of the right triangle ABC. Calculate the area of triangle ABC if the line on the hypotenuse is 0.2 dm long and if angle ∢ACS is 30°.
• Sine theorem 2
  From the sine theorem, find the ratio of the sides of a triangle whose angles are 30°, 60°, and 90°.

• Two artillery
  Objective C we observe from two artillery observatories, A and B, which are 975 m apart. The size of the BAC angle is 63°, and the size of ABC is 48°. Calculate the distance of points A and C.
• Cosine
  Cosine and sine theorem: Calculate all unknown values (side lengths or angles) from triangle ABC. c = 2.9 cm; β = 28°; γ = 14° α =? °; a =? cm; b =? cm
• Cosine
  Cosine and sine theorem: Calculate all unknown values (sides and angles) of the triangle ABC. a = 20 cm; b = 15 cm; γ = 90°; c =? cm; α =? °; β =? °
• Perpendicular forces
  Distribute the force of magnitude F = 100 N into two perpendicular components with magnitudes F1 and F2 so that the angle between forces F1 and F is 43°52'.
• Circumscribed circle ABC
  Triangle ABC, with sides a = 15 cm, b = 17.4 cm, and c = 21.6 cm, is circumscribed by a circle. Calculate the area of the segments determined by the sides of the triangle.
• 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?
• The aspect ratio
  The aspect ratio of the rectangular triangle is 13:12:5. Calculate the internal angles of the triangle.
• 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
• Parallelogram 65334
  In a parallelogram, the sum of the lengths of the sides a+b = 234. The angle subtended by the sides a and b is 60°. The diagonal size against the given angle of 60° is u=162. Calculate the sides of the parallelogram, its perimeter, and its area.

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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.