Skip to content
ToolUlkaa Tool
All tools

Mathematics

Percentage CalculatorFraction CalculatorEquation SolverTensorMatrix CalculatorUnit ConverterNumber Base ConverterDerivative CalculatorIntegral CalculatorLimit CalculatorAlgebra CalculatorQuadratic Formula CalculatorFactoring CalculatorLogarithm CalculatorSquare Root CalculatorLong Division CalculatorSignificant Figures CalculatorLCM and GCF CalculatorPrime Factorization CalculatorTriangle CalculatorPythagorean Theorem CalculatorSlope CalculatorArea CalculatorVolume CalculatorScientific CalculatorGraphing Calculator

Categories

AcademicTextMathematicsStatisticsMachine LearningAIData ScienceFile
All tools
Mathematics

AAS Triangle Calculator

Enter two angles and a non-included side to get every other side and angle.

Known values

Two angles and a side opposite one of them.

Try:

Sides a, b, c sit opposite angles A, B, C. In right mode the right angle is at C.

Area

145.7182 cm²
a = 15 cmb = 21.438 cmc = 20.317 cmA42°B73°C65°

Sides and angles

Side a
15 cm
Side b
21.4376 cm
Side c
20.3168 cm
Angle A
42°
Angle B
73°
Angle C
65°

Measures

Area (Heron's formula)
145.7182 cm²
Area (½ ab sin C)
145.7182 cm²
Perimeter
56.7545 cm
Heights (on a, b, c)
19.4291, 13.5946, 14.3446 cm
Medians (to a, b, c)
19.4916, 14.2826, 15.4626 cm
Inradius r
5.135 cm
Circumradius R
11.2086 cm
Type
acute, scalene

Solving the triangle: step by step

  1. 1Angles add to a straight angle
    C=180∘−A−BC=180^\circ-A-BC=180∘−A−B
    ↓
    C=180∘−42∘−73∘=65∘C=180^\circ-42^\circ-73^\circ=65^\circC=180∘−42∘−73∘=65∘
  2. 2Law of sines for b
    bsin⁡B=asin⁡A\dfrac{b}{\sin B}=\dfrac{a}{\sin A}sinBb​=sinAa​
    ↓
    b=15sin⁡73∘sin⁡42∘=21.4376b=\dfrac{15\sin 73^\circ}{\sin 42^\circ}=21.4376b=sin42∘15sin73∘​=21.4376
  3. 3Law of sines for c
    csin⁡C=asin⁡A\dfrac{c}{\sin C}=\dfrac{a}{\sin A}sinCc​=sinAa​
    ↓
    c=15sin⁡65∘sin⁡42∘=20.3168c=\dfrac{15\sin 65^\circ}{\sin 42^\circ}=20.3168c=sin42∘15sin65∘​=20.3168

Area, heights and circles: step by step

  1. 1Semi-perimeter
    s=a+b+c2s=\dfrac{a+b+c}{2}s=2a+b+c​
    ↓
    s=15+21.4376+20.31682=28.3772s=\dfrac{15+21.4376+20.3168}{2}=28.3772s=215+21.4376+20.3168​=28.3772
  2. 2Heron's formula
    K=s(s−a)(s−b)(s−c)K=\sqrt{s(s-a)(s-b)(s-c)}K=s(s−a)(s−b)(s−c)​
    ↓
    K=28.3772(13.3772)(6.9396)(8.0604)=145.7182K=\sqrt{28.3772(13.3772)(6.9396)(8.0604)}=145.7182K=28.3772(13.3772)(6.9396)(8.0604)​=145.7182
  3. 3Area from two sides and the angle between them
    K=12absin⁡CK=\tfrac12 ab\sin CK=21​absinC
    ↓
    K=12⋅15⋅21.4376⋅sin⁡(65∘)=145.7182K=\tfrac12\cdot 15\cdot 21.4376\cdot \sin(65^\circ)=145.7182K=21​⋅15⋅21.4376⋅sin(65∘)=145.7182

    Both methods give the same area.

  4. 4Heights
    ha=2Ka,  hb=2Kb,  hc=2Kch_a=\dfrac{2K}{a},\; h_b=\dfrac{2K}{b},\; h_c=\dfrac{2K}{c}ha​=a2K​,hb​=b2K​,hc​=c2K​
    ↓
    ha=19.4291,  hb=13.5946,  hc=14.3446h_a=19.4291,\; h_b=13.5946,\; h_c=14.3446ha​=19.4291,hb​=13.5946,hc​=14.3446
  5. 5Medians
    ma=122b2+2c2−a2m_a=\tfrac12\sqrt{2b^2+2c^2-a^2}ma​=21​2b2+2c2−a2​
    ↓
    ma=19.4916,  mb=14.2826,  mc=15.4626m_a=19.4916,\; m_b=14.2826,\; m_c=15.4626ma​=19.4916,mb​=14.2826,mc​=15.4626
  6. 6Inscribed circle
    r=Ksr=\dfrac{K}{s}r=sK​
    ↓
    r=145.718228.3772=5.135r=\dfrac{145.7182}{28.3772}=5.135r=28.3772145.7182​=5.135
  7. 7Circumscribed circle
    R=abc4KR=\dfrac{abc}{4K}R=4Kabc​
    ↓
    R=15⋅21.4376⋅20.31684⋅145.7182=11.2086R=\dfrac{15\cdot 21.4376\cdot 20.3168}{4\cdot 145.7182}=11.2086R=4⋅145.718215⋅21.4376⋅20.3168​=11.2086
  1. Tools
  2. Mathematics
  3. Triangle Calculator
  4. AAS Triangle Calculator

About AAS Triangle Calculator

This AAS triangle calculator solves a triangle from two angles and a side that is not between them. It finds the third angle from the angle sum and the other sides from the law of sines. It is free, needs no sign-up and runs in your browser, so nothing you enter is uploaded.

AAS means angle, angle, side. Here the side is a, opposite angle A, and the second angle is B. If your side is between the angles, use the ASA mode.

Knowing two angles tells you the third, so AAS and ASA are really the same problem with the side in different places.

How to use AAS Triangle Calculator

  1. 1Pick the mode that matches what you know: SSS, SAS, ASA, AAS, SSA or Right triangle.
  2. 2Type the three values in the boxes. Sides a, b, c sit opposite angles A, B, C. In right mode fill exactly two boxes.
  3. 3Choose a length unit and whether angles are in degrees or radians. Changing the angle unit converts the numbers you already typed.
  4. 4Read the sides, angles, area and other measures, and compare them with the scaled diagram.
  5. 5Open the step-by-step working to see each law of cosines or law of sines line, then Heron’s formula for the area.
  6. 6In SSA mode, check whether one solution, two solutions or none appear, and read the note that explains why.

Features

  • Six modes: SSS, SAS, ASA, AAS, SSA and right triangle.
  • Both solutions shown in the ambiguous SSA case, each with a diagram and its own working.
  • Area by Heron’s formula and by one half a b sin C, which agree.
  • Perimeter, three heights, three medians, inradius and circumradius.
  • Triangle type by angles (acute, right, obtuse) and by sides (scalene, isosceles, equilateral).
  • A scaled, labelled SVG diagram that follows light and dark mode.
  • Degrees or radians, and eight length units from millimetres to miles.
  • Clear messages when the values cannot form a triangle, instead of a wrong answer.
  • Worked examples and KaTeX formulas for every step.

Law of sines for AAS

The known side and its opposite angle set the scale for the other sides.

C = 180° − A − B
b = a sin B / sin A
c = a sin C / sin A

Worked examples

  • A = 42°, B = 73°, a = 15 → gives b = 21.4376, c = 20.3168

    C = 65°, area 145.7182.

Privacy: how it works

  • Everything is calculated by code running in your browser tab. The values you enter are not sent to Ulkaa or to any other server, and there is nothing to sign in to.

Tips

  • Check the labelling: side a is opposite angle A. Swapping a side with its neighbour gives a different triangle.
  • In SAS the angle must be the one between the two sides. If it is not, use the SSA mode.
  • If two angles already add to 180° or more, no triangle exists. The calculator says so.
  • For a right triangle you can also use SSS with the sides 3, 4 and 5 and read C = 90°.

Frequently asked questions

Is it really free?

Yes. There is no price, no trial and no credit card. Ulkaa Tool does the work with your own device, so there is no server bill to pass on to you.

Do I need an account?

No. There is no sign-up and no login. Open the page and use it. An Ulkaa account is not needed for anything on this tool.

Does it run in my browser?

Yes. Your values are processed by code running in your browser tab, on your own device.

Is my data uploaded?

No. Your values are never sent to Ulkaa or to anyone else. You can check this yourself by watching the Network tab in your browser developer tools while you use the tool.

Is AAS enough to fix a triangle?

Yes. Two angles and any one side determine the triangle uniquely, as long as the angles add to less than 180 degrees.

Which side do I enter?

The side opposite angle A, called a in this tool.

More Triangle Calculator pages

  • Triangle CalculatorEnter any three valid values and get every side, every angle, the area and a drawing of the triangle.
  • SSS Triangle CalculatorEnter three sides and get all three angles, the area and a scaled drawing.
  • SAS Triangle CalculatorEnter two sides and the angle between them to find the third side and the other angles.
  • ASA Triangle CalculatorEnter two angles and the side between them to get the other two sides and the third angle.
  • SSA Triangle CalculatorEnter two sides and a non-included angle. The calculator shows every triangle that fits.
  • Right Triangle CalculatorEnter any two values of a right triangle and get the legs, the hypotenuse, both acute angles and the area.
  • Area of a Triangle CalculatorEnter three sides to get the area by Heron’s formula, with the heights and the steps.
  • Heron’s Formula CalculatorEnter the three sides and see the semi-perimeter, the product and the area worked out.
  • Law of Sines CalculatorEnter two angles and a side to find the others with the law of sines.
  • Law of Cosines CalculatorEnter two sides and the angle between them to find the third side and the other angles.
  • Isosceles Triangle CalculatorEnter the two equal sides and the base to get the angles, the height and the area.
  • Equilateral Triangle CalculatorEnter the side length to get the height, the area and both circle radii.

Ulkaa Apps

  • Ulkaa
  • Calendar
  • Task
  • Note
  • Disk
  • Call
  • Contact
  • Mail
  • Finance
  • Health
  • Office
  • Work
  • Workspace
  • Halum
  • Jaal
  • Islam
  • Game
  • Weather
  • Campus
  • News
  • Developer
  • Help
  • Account
About·Privacy·Terms·© 2026 Ulkaa

What is Ulkaa Tool?

Ulkaa Tool is a free collection of fast, privacy-friendly online tools from Ulkaa Network. Calculate your GPA and CGPA, edit rich text, count words and characters, replace text and more — all in your browser.

Every tool runs entirely in your browser — no sign-up, and your data never leaves your device.

Academic

  • GPA Calculator
  • CGPA Calculator
  • Citation Generator
  • Quiz Maker

Text

  • Rich Text Editor
  • Word Counter
  • Character Counter
  • Text Replacement

Ulkaa

  • Ulkaa
  • Ulkaa News
  • Ulkaa Campus
  • Ulkaa Tool
  • Ulkaa Game
  • Ulkaa Weather
  • Ulkaa Islam

Company

  • About Ulkaa
  • Careers
  • Support
  • Help
  • Privacy Policy
  • Terms of Service
  • Disclaimer
  • Sitemap
© 2015-26, Ulkaa. All rights reserved.
Facebook PageLinkedIn CompanyX (Twitter) ProfileInstagram ProfileGitHub Account