If you know the values of two or more sides of a triangle, you can use the law of cosine. In the following case, you know the three sides (which in trigonometry is called SSS or side-side-side), but none of the angles. What you see here is how to solve the measurements of the three angles in the triangle ABC, which has sides where a is 7, b 8 and c is 2. You don`t know an angle and its opposite side. »; } if (chs as the first step to solve an AAS triangle? Answer YES or NO and give a reason to support your answer. Answer = “Yes. You know an angle and its opposite side. »; } if (chs as the first step to solve a SAS triangle? Answer YES or NO and give a reason to support your answer. Answer = “No. You don`t know an angle and its opposite side. »; } else if (chs as the first step to solving an SSA configuration? Answer YES or NO and give a reason to support your answer. Answer = “Yes. You know an angle and its opposite side. »; } else { // ASA str = “Can Sines` law be used as a first step to solve an ASA triangle? Answer YES or NO and give a reason to support your answer. Answer = “No.
They don`t know the angle and its opposite side. (However, it is trivial to find the remaining angle, and then you can use the law of Sines.) »; } break; Case 5: // Can the law of cosine be used as a first step in. chs = Math.random(); if (chs as the first step to solve an SSS triangle? Answer YES or NO. If the answer is YES, specify what the unknown will be in the first equation. »; Answer = “Yes. The unknown will be one of the angles. »; } if (chs as the first step to solve an AAS triangle? Answer YES or NO. If the answer is YES, specify what the unknown will be in the first equation. »; Answer = “No. (To apply the law of cosine, you need to know at least two sides.) »; } if (chs as the first step to solve a SAS triangle? Answer YES or NO. If the answer is YES, specify what the unknown will be in the first equation. »; Answer = “Yes. The unknown is the opposite side of the known angle. »; } else if (chs as the first step to solving an SSA configuration? Answer YES or NO. If the answer is YES, specify what the unknown will be in the first equation. »; Answer = “Yes (sort of). The unknown is the third side, but it is a quadratic equation in this unknown. Remember, this is the “ambiguous” case! There can be no one, one or two different triangles that satisfy a particular SSA configuration! »; } else { // ASA str = “Can the law of cosine be used as a first step to solve an ASA triangle? Answer YES or NO.
If the answer is YES, specify what the unknown will be in the first equation. »; Answer = “No. This is similar to the Pythagorean theorem except for the third term and if C is a right angle, the third term is equal to 0 because the cosine of 90° is 0 and we obtain the Pythagorean theorem. The Pythagorean theorem is therefore a special case of the cosine law. Now, use a scientific calculator to find the measurement of A. It is best to first find the angle opposite to the longest side. In this case, it is page b. “; break; Case 19: // Think about this scenario (cosine). str = “Think about this scenario: This requires some knowledge of Arccosine. (The Arccosine function will be discussed in more detail later, here you will only get basic working knowledge.) In this triangle, we know the three sides x = 5.1, y = 7.9 and z = 3.5. Use the law of cosine to find the X angle first: As you can see in the previous figure, the triangle appears to have two sharp angles and an obtuse angle, the obtuse angle opposite the longer side. 180 – (54 + 113) = 180 – 167 = 13.
The angle C measures only 13 degrees. At this point, you have been introduced to both Arcsinus and Arccosine. The arcsine “reverses the sine”. Arccosine “reverses cosine”. Let`s compare them:. Here`s another (slightly faster) way to solve an SSS triangle: Since cos B is negative, we know that B is an obtuse angle. = 11 2 + 5 2 − 2 ( 11 ) ( 5 ) ( cos 20 ° ) Given a = 11 , b = 5 and m ∠ C = 20 °. Find the remaining side and angles. B is the widest angle, so find B first with the law of cosine: Finally, we can find angle C using “the angles of a triangle total 180°”: why are we trying to find the widest angle first? In this way, the other two angles must be acute (less than 90°) and the law of sines will give correct answers.