# 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:

a

^{2}= b

^{2}+ c

^{2}- 2bc * cos(A)

c

^{2}= a

^{2}+ b

^{2}- 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:

- Determine 18223

From the sine theorem, determine the ratio of the sides of a triangle whose angles are 30 °, 60 °, and 90 °. - Largest angle of the triangle

Calculate the largest angle of the triangle whose sides have the sizes: 2a, 3/2a, 3a - 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 - The aspect ratio

The aspect ratio of the rectangular triangle is 13:12:5. Calculate the internal angles 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? - Rhomboid

The rhomboid sides' dimensions are a= 5cm, b = 6 cm, and the angle's size at vertex A is 60°. What is the length of the side AC? - 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 - 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). - 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 - 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. - Observer

The observer sees a straight fence 100 m long in 30° view angle. From one end of the fence is 102 m. How far is it from another end of the fence? - 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. - Mast shadow

The mast has a 13 m long shadow on a slope rising from the mast foot in the direction of 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.

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#### 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