Name: solving oblique triangles with sines
Uploaded: 2025-11-26T05:44:32.000Z
Duration: 1 min 29 s
Channel: JoVE

既知の水平距離で離れた2つの観測所は、既知の仰角で衛星を観測します。最初のステーションから衛星までの距離はわかっています。目標は、2つのステーションと衛星によって形成された三角形を解くことによって、衛星から2番目のステーションまでの距離を見つけることです。片側と2つの角度がわかっている場合、または2つの辺とそのうちの1つと反対の角度が提供されている場合、正弦の法則が適用されます。正弦の法則によれば、三角形全体で辺の長さと反対角の正弦の比率は一定のままです。この場合、片側 c と2つの角度 C と B がわかっています。これは正弦の法則に適合し、 辺 b の計算を可能にします。別の例を挙げてみましょう。正弦の法則は、川の対岸にある2つの旗の間の距離を見つけるために使用できます。ここで、BC側は100メートル、反対の角度Aは30度です。別の既知の角度は、未知の側ACの反対側の70度のBです。正弦の法則を使用して、角度 A の BC を使用して、角度 B の AC を見つけます。この結果は、側面 のACに沿った2つの旗間の傾斜距離です。

正弦定理

The Law of Sines

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Education

JoVE Core

Math Fundamentals

数学の基礎

Unit

ユニット

Trigonometry

三角法

KEY TERMS AND CONCEPTS

主要用語と概念

solving oblique triangles with sines

Solving oblique triangles uses the Law of Sines. An oblique triangle is a triangle with no right angle. These triangles need a different trigonometric method because the Pythagorean theorem works only for right triangles.

The Law of Sines links each side of a triangle to the sine of its opposite angle. In triangle ABC, side a is opposite angle A, side b is opposite angle B, and side c is opposite angle C. The ratios a/sin A, b/sin B, and c/sin C are constant.

This relationship helps find unknown sides or unknown angles when enough information is known. It is especially useful when two angles and any one side are given. It also works when two sides and the angle opposite one of them are known.

The Law of Sines is useful in navigation, surveying, and astronomy. In these fields, direct measurement of every part of a triangle may not be possible. The law makes it easier to solve non-right triangles and find missing measurements.

Solving Oblique Triangles with Sines

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the law of sines

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key terms and concepts

Learn how the Law of Sines helps solve oblique triangles by linking sides and angles. Useful for finding missing measurements in non-right triangles.

Solving Oblique Triangles with Sines | JoVE K12

The JoVE Math Fundamentals collection is designed to build a deep and comprehensive understanding of essential mathematics. Covering the foundations of algebra, geometry, trigonometry, and analytic reasoning, this course establishes a strong base for future studies. The collection connects core mathematical concepts with real-world practice, equipping learners to solve complex problems, master problem-solving skills, and apply abstract ideas.

math fundamentals

Solving Oblique Triangles with Sines

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