SSS: If the three sides of a triangle are known, first use the Law of Cosines to find one of the angles. It is usually best to find the largest angle first, the one opposite the longest side. Then, set up a proportion using the Law of Sines to find the second angle.

## How do you find an angle when you have all three sides?

“SSS” is when we know three sides of the triangle, and want to find the missing angles.

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To solve an SSS triangle:

- use The Law of Cosines first to calculate one of the angles.
- then use The Law of Cosines again to find another angle.
- and finally use angles of a triangle add to 180° to find the last angle.

## How do you find the largest angle?

The largest angle is 5 times the smallest angle, so the largest angle is 5x degrees. So the smallest angle measures 24 degrees.

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words | check |
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The third angle is 12 degrees more than the smallest angle. | Is 36 equal to 12 more than 24? Yes! |

This is a triangle: do the angles all add up to 180 degrees? | 24 + 36 + 120 = 180 |

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

If you know two sides and the angle between them, use the cosine rule and plug in the values for the sides b, c, and the angle A. Next, solve for side a. Then use the angle value and the sine rule to solve for angle B. Finally, use your knowledge that the angles of all triangles add up to 180 degrees to find angle C.

## Which is the largest angle in a triangle?

Can you determine which angle is the largest? The largest angle will be opposite 18 because that is the longest side. Similarly, the smallest angle will be opposite 7, which is the shortest side.

## How do you find an angle of a triangle with 3 sides?

Find the angle of elevation of the plane from point A on the ground.

- Step 1 The two sides we know are Opposite (300) and Adjacent (400).
- Step 2 SOHCAHTOA tells us we must use Tangent.
- Step 3 Calculate Opposite/Adjacent = 300/400 = 0.75.
- Step 4 Find the angle from your calculator using tan-1

## Can you solve a triangle with 3 angles?

“AAA” is when we know all three angles of a triangle, but no sides. AAA triangles are impossible to solve further since there is nothing to show us size … we know the shape but not how big it is. We need to know at least one side to get any further … that’s life!

## Which side of XYZ is the longest?

Answer: XY is the longest side in the given ΔXYZ.

## Which type of angle is the largest?

A reflex angle is the larger angle, it’s always more than 180° (half a circle) but less than 360° (A full circle).

## How do you find the side of a triangle given two sides and an angle?

“SAS” is when we know two sides and the angle between them. use The Law of Cosines to calculate the unknown side, then use The Law of Sines to find the smaller of the other two angles, and then use the three angles add to 180° to find the last angle.

## What are the sides of angle?

The sides of an angle refer to the two rays or line segments that form the angle. In the figure below, rays BA and BC are the sides of angle ABC. An angle is formed by rotating a ray around its endpoint.

## How do you figure out angles?

The formula for finding the total measure of all interior angles in a polygon is: (n – 2) x 180. In this case, n is the number of sides the polygon has. Some common polygon total angle measures are as follows: The angles in a triangle (a 3-sided polygon) total 180 degrees.

## Which is the shortest side in right angle triangle?

In any triangle, the longest side is opposite the largest angle, and the shortest side is opposite the smallest angle. Thus, in a right triangle, the hypotenuse is always the longest side.

## Do all triangles equal 180 degrees?

The answer is yes! To mathematically prove that the angles of a triangle will always add up to 180 degrees, we need to establish some basic facts about angles. The first fact we need to review is the definition of a straight angle: A straight angle is just a straight line, which is where it gets its name.

## What angle is opposite the longest side?

The hypotenuse is always the longest side in a right triangle because it is opposite of the largest angle, the ninety degree angle.