Triangle Calculator with Angle-Side-Angle (ASA)

Triangle Calculator (2 Angles and 1 Side)


How to Use the Triangle Calculator with Angle-Side-Angle (ASA)

This Triangle Calculator with Angle-Side-Angle (ASA), where you know two angles and one side. By entering your known values, the calculator quickly computes the remaining angles, sides, and other properties of the triangle. Here’s a step-by-step guide on how to use it effectively.

Step 1: Enter Your Known Values

  1. Input the First Angle:
  • In the calculator, enter the measurement of one of the given angles, let’s call it Angle B.
  • Ensure that the angle is in degrees. If your angle is in radians, you’ll need to convert it to degrees.
  1. Input the Second Angle:
  • Now, enter the second known angle, called Angle C.
  • The calculator automatically sums the angles to ensure they are consistent with a valid triangle. The sum of angles in any triangle must be exactly 180°.
  1. Input the Known Side:
  • Finally, input the length of the side opposite one of the given angles. Let’s call this side a.
  • This is essential for the calculator to use the Law of Sines to find the other sides.

Step 2: Calculate the Missing Third Angle

  • Once you enter two angles, the calculator finds the missing Angle A by subtracting the sum of the known angles from 180°.
  • This step is essential as it provides the final angle, completing the triangle’s angle measurements.

Step 3: Calculate the Remaining Sides Using the Law of Sines

The calculator applies the Law of Sines to calculate the lengths of the missing sides ( b ) and ( c ).

Using the formula:

a​/sin (A) = b/sin (B) = c​/sin (C)

It finds side ( b ) by rearranging:

b=a⋅sin (B)​/sin (A)

Similarly, it finds side ( c ) as:

c=a⋅sin(C)/sin(A)​

Step 4: Calculate Additional Triangle Properties

  1. Perimeter:

Once all sides ( a ), ( b ), and ( c ) are known, the perimeter ( P ) is calculated as:

P = a + b + c

  1. Area:

The area of the triangle is calculated using the Side-Angle-Side formula:

​Area=1/2 ​x a x b x sin(C)

  1. Medians:

The length of each median (a line from a vertex to the midpoint of the opposite side) is calculated. For example:

Median from A=1​/2 √2b2+2c2−a2

  1. Heights:

The calculator provides the height from each vertex to its opposite side, calculated as:

Height from A=2 x Area​ / a

  1. Inradius and Circumradius:

Inradius ( r ) (the radius of the inscribed circle) is calculated as:

r = Area ​/ semi-perimeter

Circumradius ( R ) (radius of the circumscribed circle) is calculated as:

R = a​ / 2 sin (A)

  1. Centroid:
  • The calculator locates the centroid, which is the intersection point of the medians. If coordinate inputs are available, the centroid is found by averaging the coordinates of the vertices.

Step 5: Review Results

  • Detailed Output:
  • The calculator displays all results in a clear, organized manner. You’ll see values for:
    • All three angles
    • All three side lengths
    • Perimeter and area
    • Medians and heights
    • Inradius, circumradius, and centroid
  • Graphical Representation (if available):
  • Some calculators may provide a visual representation of the triangle based on your inputs, helping you better understand the calculated values in a real-world context.

Example for Triangle Calculator with Angle-Side-Angle (ASA)

Suppose you know:

  • Angle B = 45°
  • Angle C = 60°
  • Side a (opposite Angle A) = 10 cm

Here’s how the calculator works:

Calculates Angle A:

A = 180° – (45° + 60°) = 75°

Calculates Side b:

b = 10⋅sin(45°) / sin(75°)​ ≈ 7.32 cm

Calculates Side c:

c = 0⋅sin(60°)​ / sin(75°)1 ≈ 8.66 cm

Calculates Perimeter:

P = 10 + 7.32 + 8.66 = 25.98 cm

Calculates Area:

Area = 1​/2 ⋅ 10 ⋅ 7.32 ⋅ sin(60°) ≈ 31.75 cm2

The calculator handles these calculations efficiently, giving accurate results for all triangle properties based on the initial Triangle Calculator with Angle-Side-Angle (ASA).

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