# When using the law of sines, why can the ssa case result in zero, one, or two triangles? Explain.

## How do you determine if you have 0 1 or 2 triangles for the ambiguous case?

To determine if there is a 2nd valid angle:

1. See if you are given two sides and the angle not in between (SSA). …
2. Find the value of the unknown angle.
3. Once you find the value of your angle, subtract it from 180° to find the possible second angle.
4. Add the new angle to the original angle.

## Can we use the law of sines in SSA case?

“SSA” is when we know two sides and an angle that is not the angle between the sides. use The Law of Sines first to calculate one of the other two angles; then use the three angles add to 180° to find the other angle; finally use The Law of Sines again to find the unknown side.

## How do you use the ambiguous case in law of sines?

The Ambiguous Case of the Law of Sines

1. See if you are given two sides and the angle not in between (SSA). This is the situation that may have 2 possible answers.
2. Find the value of the unknown angle.
3. Once you find the value of your angle, subtract it from 180° to find the possible second angle.
4. Add the new angle to the original angle.

## What are the two cases in which the laws of sines can be applied to solve a non right triangle?

The Law of Sines can be used to solve oblique triangles, which are non-right triangles. According to the Law of Sines, the ratio of the measurement of one of the angles to the length of its opposite side equals the other two ratios of angle measure to opposite side. There are three possible cases: ASA, AAS, SSA.

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## How do you determine the number of triangles in an ambiguous case?

In the ambiguous case we first find the height by using the formula h=bsinA . Note that A is the given angle and its side is always a so the other side will be b . htriangles. htriangle.

## Is SSA a congruence theorem?

Given two sides and non-included angle (SSA) is not enough to prove congruence. … But there are two triangles possible that have the same values, so SSA is not sufficient to prove congruence. In the figure above, the two triangles above are initially congruent.

## What is the law of cosines used for?

The law of cosines allows us to find angle (or side length) measurements for triangles other than right triangles. The third side in the example given would ONLY = 15 if the angle between the two sides was 90 degrees. In the example in the video, the angle between the two sides is NOT 90 degrees; it’s 87.

## Why is SSA called the ambiguous case?

Working with the third option of SSA, however, leaves the door open for several different situations and solutions to occur. For this reason, SSA is referred to as the Ambiguous Case. Ambiguous means open to two or more interpretations. SSA: If two sides and the non-included angle are given, three situations may occur.

## How do you know if it is the ambiguous case?

Explanation:

• If angle A is acute, and a
• If angle A is acute, and a = h, one possible triangle exists.
• If angle A is acute, and a > b, one possible triangle exists.
• If angle A is acute, and h

## What is the rule of sin?

Sine Rule. The Sine Rule can be used in any triangle (not just right-angled triangles) where a side and its opposite angle are known. You will only ever need two parts of the Sine Rule formula, not all three. You will need to know at least one pair of a side with its opposite angle to use the Sine Rule.

## How do you know whether to use law of sines or cosines?

The sine rule is used when we are given either a) two angles and one side, or b) two sides and a non-included angle. The cosine rule is used when we are given either a) three sides or b) two sides and the included angle.

## Is SOH CAH TOA only for right triangles?

Q: Is sohcahtoa only for right triangles? A: Yes, it only applies to right triangles. … A: They hypotenuse of a right triangle is always opposite the 90 degree angle, and is the longest side.

## Is Pythagorean theorem only for right triangles?

Pythagoras’ theorem only works for right-angled triangles, so you can use it to test whether a triangle has a right angle or not.