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##### 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

**know three sides**ofthe

**triangle**, and want to find the missing

**angles**.

**To solve an SSS triangle:**

- use The Law of Cosines first to calculate one ofthe
**angles**. - then use The Law of Cosines again to findanother
**angle**. - 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 **angle**isthe length of the adjacent **side** divided by thehypotenuse,or the **sine** of an **angle** is the opposite**side**divided by the hypotenuse. In your case, you know the**side**opposite 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 exterior**angle 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?

**Example**

- Step 1 The two sides we know are Adjacent (6,750) andHypotenuse(8,100).
- Step 2 SOHCAHTOA tells us we must use Cosine.
- Step 3 Calculate Adjacent / Hypotenuse = 6,750/8,100=0.8333.
- 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**.To**find** the length of leg a, substitute the known valuesintothe Pythagorean Theorem. Solve for a^{2}.