How to do law of sines and cosines

How do you do law of sines?

In ΔABC is an oblique triangle with sides a,b and c , then asinA=bsinB=csinC . 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).

Is SSS law of cosines?

The Law of Cosines states that: Use the law of cosines when you are given SAS, or SSS, quantities. For example: If you were given the lengths of sides b and c, and the measure of angle A, this would be SAS. SSS is when we know the lengths of the three sides a, b, and c.

What is the equation for the law of cosines?

The cosine of a right angle is 0, so the law of cosines, c2 = a2 + b2 – 2ab cos C, simplifies to becomes the Pythagorean identity, c2 = a2 + b2, for right triangles which we know is valid.

Where is angle of depression?

The angle of depression is the angle between the horizontal line of sight and the line of sight down to an object. For example, if you were standing on top of a hill or a building, looking down at an object, you could measure the angle of depression.

When can we use law of sines?

When to Use the Law of Sines

The Law of Sines is utilized whenever you have either Angle-Side-Angle (ASA) or Angle-Angle-Side (AAS) congruency. In fact, we will also learn one more type of congruency that the Law of Sines can be used in our next lesson titled the Ambiguous Case.

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SSS (side-side-side) All three corresponding sides are congruent. SAS (side-angle-side) Two sides and the angle between them are congruent. ASA (angle-side-angle)

Can you solve a SSS triangle?

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.

Is SAS sine or cosine?

“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.

How is the law of cosines proven?

The Law of Cosines is a theorem which relates the side-lengths and angles of a triangle. It can be derived in several different ways, the most common of which are listed in the “proofs” section below. It can be used to derive the third side given two sides and the included angle.

Why does the law of cosines work?

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.

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Does the law of cosines work for any triangle?

It works on any triangle, not just right triangles. where a and b are the two given sides, C is their included angle, and c is the unknown third side. See figure above.

What is the angle of depression in a triangle?

If a person stands and looks down at an object, the angle of depression is the angle between the horizontal line of sight and the object. Trigonometry can be used to solve problems that use an angle of elevation or depression.

What does the angle of depression mean?

: the angle formed by the line of sight and the horizontal plane for an object below the horizontal.

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