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Ch. 7 - Applications of Trigonometry and Vectors
Lial - Trigonometry 12th Edition
Lial12th EditionTrigonometryISBN: 9780136552161당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Lial 12th EditionCh. 7 - Applications of Trigonometry and Vectors문제 4
8장, 문제 4

CONCEPT PREVIEW Assume a triangle ABC has standard labeling.


a. Determine whether SAA, ASA, SSA, SAS, or SSS is given.


b. Determine whether the law of sines or the law of cosines should be used to begin solving the triangle.


a, B, and C

검증된 단계별 안내
1
Step 1: Identify the given parts of the triangle. The problem states that sides and angles given are 'a', 'B', and 'C'. Here, 'a' is the side opposite angle 'A', and 'B' and 'C' are two angles of the triangle.
Step 2: Determine the type of information given. Since two angles (B and C) and one side (a) are known, this corresponds to the SSA (Side-Side-Angle) case, because you have one side and two angles, but the side is not between the two known angles.
Step 3: Recall the criteria for each case: SAA (two angles and a non-included side), ASA (two angles and the included side), SSA (two sides and a non-included angle), SAS (two sides and the included angle), and SSS (three sides). Since you have two angles and one side opposite an unknown angle, this is SSA.
Step 4: Decide which law to use. The Law of Sines is typically used when you have an angle-side opposite pair and another angle or side, which fits the SSA case here.
Step 5: Conclude that to begin solving the triangle with given 'a', 'B', and 'C', you should use the Law of Sines, which is given by the formula: \(\frac{a}{\sin\left( A \right)} = \frac{b}{\sin\left( B \right)} = \frac{c}{\sin\left( C \right)}\).

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이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Triangle Congruence and Similarity Criteria

Triangle congruence criteria such as SAA (or AAS), ASA, SSA, SAS, and SSS describe specific combinations of sides and angles that determine a unique triangle. Understanding these helps identify what information is given and what methods apply for solving the triangle.
추천 영상:
5:35
30-60-90 Triangles

Law of Sines

The Law of Sines relates the ratios of sides to the sines of their opposite angles in any triangle. It is especially useful when two angles and one side (AAS or ASA) or two sides and a non-included angle (SSA) are known, allowing for the determination of unknown sides or angles.
추천 영상:
가이드 코스
4:27
Intro to Law of Sines

Law of Cosines

The Law of Cosines generalizes the Pythagorean theorem for any triangle, relating the lengths of sides to the cosine of an included angle. It is typically used when two sides and the included angle (SAS) or all three sides (SSS) are known, enabling calculation of unknown sides or angles.
추천 영상:
가이드 코스
4:35
Intro to Law of Cosines
관련 실천
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교과서 질문

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교과서 질문

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