Can we use the law of sine?

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Can we use the law of sine?

The law of sine can Used to calculate the remaining sides of a triangle when two angles and one side are known– A technique called triangulation. It can also be used when two sides and an open angle are known.

Can you use the law of sine all the time?

the law Sine always « works » when you have all acute angles. We only have a problem when the angle in question is an obtuse angle. …so it all boils down to the fact that the calculator can’t figure out if you need an obtuse angle when solving for x using the law of sine!

When can’t the law of sine be used?

if we were Two sides and an included angle of a given triangle Or if given 3 sides of a triangle, we can’t use the law of sine because we can’t establish any scale given enough information.

How does the law of sine apply in real life?

A practical application of the rule of sine is the sine bar, which Used to measure the inclination angle in engineering. Other common examples include measuring distances in navigation and measuring the distance between two stars in astronomy.

Can the law of sine be used for any triangle?

The law of sine can be used for any triangle (not just right triangles), where An edge and its opposite angle are known. You will only need two parts of the sine rule formula, not all three. You need to know at least one pair of sides with opposite angles to use the sine rule.

The Law of Sines, Basic Introduction, AAS and SSA – One Solution, Two Solutions and No Solution, Trigonometric Functions

32 related questions found

Where is the law of sine used?

The law of sine can be used Calculate the remaining sides of a triangle when two angles and one side are known– A technique called triangulation. It can also be used when two sides and an open angle are known.

Does the law of cosines only apply to right triangles?

The law of cosines is a tool for solving triangles. That is, given some information about a triangle, we can find out more. …from there, you can use the law of cosines to find the third side. It works for any triangle, more than a right triangle.

How do you answer the law of sine?

The Law of Sines is a useful rule that shows the relationship between the angles of a triangle and the length of the opposite side. The sine of an angle divided by the length of the opposite side is the same For each corner of a triangle and its opposite side.

How does the sine rule work?

To solve a triangle is to find the length of each of its sides and all of its angles.The rule of sine is used when we give a) two angles and a side, or b) sides and a non-included angle. Use the cosine rule when we give a) three sides or b) two sides and an angle.

What angle is opposite the longest side?

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

How do you know if the law of sine has two solutions?

if Their sum is less than 180°, you have two valid answers. If the sum exceeds 180°, the second angle has no effect.

Which is the depression angle?

If a person is standing looking down at an object, the depression angle is The angle between the horizontal line of sight and the object. Trigonometric functions can be used to solve problems using either elevation or depression.

What is the shortest side of a 30 60 90 triangle?

Explanation: In a 30-60-90 right triangle, the shortest side opposite the 30 degree angle is half of the hypotenuse.

Is AAS the sine law?

« AAS » means we know both angles and one side (not between angles).then the law Sine finds each of the other sides.

Is SAS the law of cosines?

When you have two sides of a triangle and the angle between them, also known as SAS (side-angle-side), you can use cosine Solve the other three parts.

What is the law of sine cosines?

The Law of Sines establishes the relationship between the angle and side length of ΔABC: a/sin(A) = b/sin(B) = c/sin(C). This shows that cosine, unlike sine, changes its sign from 0° – 180° of the effective angle of the triangle. …

Why is sin used in Snell’s Law?

Most people are familiar with Snell’s Law because their legs are observed to shorten significantly when standing in water. … Snell’s Law states that The ratio of the sine of the angle of incidence and the angle of transmission is equal to the ratio of the refractive indices of the materials at the interface.

What is the law of cosines used for?

The law of cosines is used for Find the rest of an oblique (non-right angled) triangle when the length of the two sides and the measure of the included angle are known (SAS) Or the length of the three sides (SSS) is known.

What is a AAA triangle?

« AAA » means « angle, angle, angle » « AAA » is when We know all three angles of a triangle, but no sidesThe .AAA triangle can’t be solved further because nothing tells us the size… we know the shape, but not how big it is.

Does the law of cosines always work?

cosine law It’s great for solving triangles when you have two sides and an angle, but the angles are not on the sides. …Also, to solve an SSA (or corner) triangle using the law of cosines, you have to be careful to find the correct triangle – there are two possibilities.

Can you use the Pythagorean theorem on non-right triangles?

Solving Oblique Triangles Using the Law of Cosines

Three formulas make up the law of cosines. …the derivation begins with the generalized Pythagorean theorem, which is an extension of the Pythagorean theorem to non-right triangles.

Can you use SOH CAH TOA for any triangle?

Q: Does sohcahtoa only work with right triangles? A: yes it only works for right triangles. … A: The hypotenuse of a right triangle is always opposite to a 90-degree angle, and is the longest side.

Who discovered the law of cosines?

In the 15th century, Jamshed CashPersian mathematician and astronomer, who provided the first explicit statement of the law of cosines in a form suitable for triangulation. He provided an accurate trigonometric table and expressed the theorem in a form suitable for modern use.

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