# Triangle calculator SAS

Please enter two sides of the triangle and the included angle

If you know the lengths of two sides (a and b) and the angle (C) between them, you can use the Law of Cosines to find the length of the third side (c) as:

c

^{2}= a

^{2}+ b

^{2}- 2ab * cos(C)

Once you have the length of the third side, you can use the Law of Sines to find the remaining angles (A and B) 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 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 A is 47°, find side a. Please round to one decimal. - Triangle SAS

Calculate the triangle area and perimeter if the two sides are 105 dm and 68 dm long and angle them clamped is 50 °. - Scalene triangle

Solve the triangle: A = 50°, b = 13, c = 6 - Vector sum

The magnitude of the vector u is 12 and the magnitude of the vector v is 8. The angle between vectors is 61°. What is the magnitude of the vector u + v?

- Greatest angle

Calculate the greatest triangle angle with sides 124, 323, 302. - Diagonals

Calculate the length of the rhombus's diagonals if its side is long 5 and one of its internal angles is 80°. - The aspect ratio

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

In △ABC a=6, b=6 and ∠C=110°. Calculate the length of the side c. - 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.

- A rhombus

A rhombus has sides of the length of 10 cm, and the angle between two adjacent sides is 76 degrees. Find the length of the longer diagonal of the rhombus. - Calculate 2

Calculate the largest angle of the triangle whose sides are 5.2cm, 3.6cm, and 2.1cm - 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. - 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).

- ABCD

AC= 40cm , angle DAB=38 , angle DCB=58 , angle DBC=90 , DB is perpendicular on AC , find BD and AD - Isosceles 83157

Using the cosine theorem, prove that in an isosceles triangle ABC with base AB, c=2a cos α. - Four sides of trapezoid

In the trapezoid ABCD is |AB| = 73.6 mm; |BC| = 57 mm; |CD| = 60 mm; |AD| = 58.6 mm. Calculate the size of its interior angles.

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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