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

Last Updated: 11th May, 2020

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"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.

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?

Example

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. Professional

## How do you find the degree of an angle?

To calculate angles in a polygon, first learnwhatyour angles add up to when summed, like 180degrees ina triangle or 360 degrees in aquadrilateral. Once you knowwhat the angles add up to, addtogether the angles youknow, then subtract the answer fromthe total measures of theangles for yourshape. Professional

## What is sine rule for Triangle?

The Sine Rule
The Law of Sines (sine rule) is animportantrule relating the sides and angles of anytriangle(it doesn't have to be right-angled!): If a, b and care thelengths of the sides opposite the angles A, B and C inatriangle, then: a = b = c. sinAsinBsinC. Professional

## What do the sides of a triangle add up to?

Since the three interior angles of a triangle addupto 180 degrees, in a right triangle, since one angleisalways 90 degrees, the other two must always add up to90degrees (they are complementary). The side oppositetheright angle is called the hypotenuse. The sides adjacenttothe right angle are the legs. Explainer

## How do you use the law of sines?

Simply, it states that the ratio of the length of asideof a triangle to the sine of the angle opposite thatside isthe same for all sides and angles in a given triangle.InΔABC is an oblique triangle with sides a,b and c ,thenasinA=bsinB=csinC . Explainer

## How do we find the perimeter of a triangle?

Finding the Perimeter When Three Side LengthsareKnown. Remember the formula for finding the perimeter ofatriangle. For a triangle with sides a, b and c,theperimeter P is defined as: P = a + b + c. Explainer

## What are the angles of an equilateral triangle?

Here's an example of an equilateraltriangle:You'll notice that along with this triangle'ssides, itsthree angles are also all equal. Since the sum ofatriangle's angles is always 180 degrees, eachanglein an equilateral triangle must measure60degrees. Pundit

## What makes a right triangle?

A right triangle (American English)orright-angled triangle (British English) isatriangle in which one angle is a right angle(thatis, a 90-degree angle). The side opposite the rightangle iscalled the hypotenuse (side c in the figure). Pundit

## What is the angle of a right triangle?

The right triangle has one 90 degreeangleand two acute (< 90 degree) angles. Since thesum of theangles of a triangle is always 180 degreesy + z = 90degrees. The two sides of the triangle that are bytheright angle are called the legs and the side opposite oftheright angle is called the hypotenuse. Pundit

## What is the area of the right triangle?

A = (1/2)bh, where A is the area ofthetriangle, b is the length of the base and h is the heightofthe triangle; However, with a right triangle,it'smuch more convenient in finding its area if we utilizethelengths of the two legs (the two sides that are shorter thanthelongest side, the hypotenuse and that are Pundit

## What is the definition of sine in math?

In mathematics, the sine is atrigonometricfunction of an angle. The sine of an acuteangle isdefined in the context of a right triangle: for thespecifiedangle, it is the ratio of the length of the side that isoppositethat angle to the length of the longest side of thetriangle (thehypotenuse). Teacher

## How do you find the degree of an angle without a protractor?

To measure an acute angle without aprotractor,start by drawing a vertical line connecting the 2rays of theangle to form a right triangle. Note that theangleformed by the adjacent side of the triangle and theopposite sidemeasures 90 degrees. Next, measure thelength of theadjacent side to find the run. Teacher

## How do you find the height of a right triangle?

If you know the base and area of the triangle,youcan divide the base by 2, then divide that by the area tofindthe height. To find the height of anequilateraltriangle, use the Pythagorean Theorem, a^2 + b^2=c^2. Teacher

## How many degrees is a right angle?

90 degrees Reviewer

## How do you find sine?

The sine function, along with cosine andtangent,is one of the three most common trigonometric functions. Inanyright triangle, the sine of an angle x is the length oftheopposite side (O) divided by the length of the hypotenuse (H).In aformula, it is written as 'sin' without the 'e': Reviewer

## Which side is opposite and adjacent?

Before getting stuck into the functions, it helps togivea name to each side of a right triangle:"Opposite" isopposite to the angle θ"Adjacent" isadjacent (next to) to the angle θ"Hypotenuse" is thelong one. Reviewer

## What is the formula for any triangle?

The general formula for the area ofatriangle is well known. The area of a triangle canbeexpressed using the lengths of two sides and the sine oftheincluded angle. AreaΔ = ½ absinC. Reviewer

## How many triangles are there?

Most people on Quora agreed that the answer is 24,witheach row containing six triangles. However, if youreallywant to get technical, the truly “correct” answeris25. The 25th triangle is hidden in the 'A'inthe artist's signature in theright-handcorner. Supporter

## How do you bisect an angle?

Construction: bisect ∠ABC.
1. STEPS:
2. Place compass point on the vertex of the angle (point B).
3. Stretch the compass to any length that will stay ONtheangle.
4. Swing an arc so the pencil crosses both sides (rays) ofthegiven angle.
5. Place the compass point on one of these new intersectionpointson the sides of the angle. Supporter

## How do you work out missing angles in a triangle?

Step 2: Add together the two known anglesinsidethe triangle. To determine to measure of theunknownangle, be sure to use the total sum of 180°. Iftwoangles are given, add them together and then subtractfrom180°. If two angles are the same and unknown,subtractthe known angle from 180° and then divideby2. Co-Authored By:

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11th May, 2020

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