In which cases can we use law of sines?

The law of sines can be used to compute the remaining sides of a triangle when two angles and a side are known—a technique known as triangulation. It can also be used when two sides and one of the non-enclosed angles are known.

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 is the law of sines used in real-life?

One real-life application of the sine rule is the sine bar, which is used to measure the angle of tilt in engineering. Other common examples include measuring distances in navigation and the measurement of the distance between two stars in astronomy.

In what cases can you apply the law of cosines?

When to Use The Law of Cosines is useful for finding: the third side of a triangle when we know two sides and the angle between them (like the example above) the angles of a triangle when we know all three sides (as in the following example)

How do you use the law of sines?

In Δ A B C is an oblique triangle with sides a , b and c , then a sin A = b sin B = c sin C . To use the Law of Sines you need to know either two angles and one side of the triangle (AAS or ASA) or two sides and an angle opposite one of them (SSA).

Which is the ambiguous case of the law of sines?

There are six different scenarios related to the ambiguous case of the Law of sines: three result in one triangle, one results in two triangles and two result in no triangle. We’ll look at three examples: one for one triangle, one for two triangles and one for no triangles. Then, we find sin − 1(0.4945) ≈ 29.6 ∘.

How is the sine law used to find unknown angles?

The sine law is used to find the unknown angle or unknown side. As per the law, we know, if a, b and c are the lengths of three sides of a triangle and ∠A, ∠B and ∠C are the angles between the sides, then; Now if suppose, we know the value of one of the side, and the value of two angles, such as: find b?

How are the sines of an angle equal?

Not really, look at this general triangle and imagine it is two right-angled triangles sharing the side h: The sine of an angle is the opposite divided by the hypotenuse, so: a sin (B) and b sin (A) both equal h, so we get: a sin (B) = b sin (A)