Asked by: Norayr Flickenschildt
hobbies and interests drawing and sketching

How do you find the angles of a triangle knowing 3 sides?

Last Updated: 11th May, 2020

"SSS" is when we know three sides ofthetriangle, and want to find the missing angles.

To solve an SSS triangle:
  1. use The Law of Cosines first to calculate one oftheangles.
  2. then use The Law of Cosines again to findanotherangle.
  3. and finally use angles of a triangle add to 180°tofind the last angle.

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Keeping this in consideration, how do you find the angles of a triangle when you know the sides?

Answer: Use the fact that the cos of an angleisthe length of the adjacent side divided by thehypotenuse,or the sine of an angle is the oppositesidedivided by the hypotenuse. In your case, you know thesideopposite the angle.

Furthermore, how do you find the angle of a triangle? The interior angles of a triangle always add upto180° while the exterior angles of a triangle areequal tothe sum of the two interior angles that are notadjacent toit. Another way to calculate the exteriorangle of atriangle is to subtract the angle of thevertex ofinterest from 180°.

Accordingly, how do you find the angle of a right triangle with 3 sides?


  1. Step 1 The two sides we know are Adjacent (6,750) andHypotenuse(8,100).
  2. Step 2 SOHCAHTOA tells us we must use Cosine.
  3. Step 3 Calculate Adjacent / Hypotenuse = 6,750/8,100=0.8333.
  4. Step 4 Find the angle from your calculatorusingcos-1 of 0.8333:

How do you find the missing side of a triangle?

The hypotenuse is always opposite the right angle anditis always the longest side of the triangle.Tofind the length of leg a, substitute the known valuesintothe Pythagorean Theorem. Solve for a2.

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