Name: measuring rocket height with trigonometry
Uploaded: 2025-11-26T05:44:33.000Z
Duration: 1 min 19 s
Channel: JoVE

한 사람이 로켓에서 고정된 거리에 서서 수직 발사를 준비합니다.로켓이 위쪽으로 이동함에 따라 로켓의 위치와 앙각은 비행 중에 지속적으로 변합니다.삼각 함수는 이러한 변화하는 각도를 로켓의 수직 높이, 절대 거리 및 지상 거리와 연결합니다.탄젠트 함수는 로켓의 수직 높이를 관측된 각도 및 고정된 지상 거리와 연관시킵니다.로켓의 높이는 알려진 지상 거리에 측정된 각도의 탄젠트를 곱하여 구합니다.각도의 사인은 로켓의 수직 높이와 절대 거리의 비율을 나타내고, 코사인은 지상 거리와 절대 거리의 비율을 나타냅니다.수직 높이를 알게 되면 사인은 높이를 사용하여 절대 거리를 계산할 수 있고 코사인은 지상 거리를 사용하여 동일한 작업을 수행할 수 있습니다.각도가 증가함에 따라 이러한 삼각 관계는 계산된 높이와 로켓까지의 관측 거리 모두에 영향을 미칩니다.이러한 기능을 적용함으로써 관찰자는 측정된 각도에서 로켓의 높이, 절대 거리 및 지상 거리를 삼각 측량할 수 있습니다.

삼각함수: 문제 해결

Trigonometric Functions: Problem Solving

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&#47196;&#53011; &#48156;&#49324;&#50752; &#44057;&#51060; &#44256;&#51221;&#46108; &#51648;&#47732; &#50948;&#52824;&#50640;&#49436; ...

Education

교육

JoVE Core

Math Fundamentals

수학 기초

Unit

단위

Trigonometry

삼각법

KEY TERMS AND CONCEPTS

주요 용어 및 개념

삼각 함수: 문제 해결

measuring rocket height with trigonometry

Measuring rocket height with trigonometry uses a fixed ground point and a changing angle of elevation. An observer stands a known horizontal distance from the launch site and watches the object rise. The angle between the ground and the line of sight gives the key information for finding height.

The tangent function is the main tool for this calculation. Tangent is the ratio of the vertical side to the adjacent side in a right triangle. When the ground distance is fixed, the object’s height equals the horizontal distance multiplied by the tangent of the measured angle.

Sine and cosine also describe the same triangle. Sine shows the ratio of the height to the slanted line of sight. Cosine shows the ratio of the ground distance to that same slanted distance.

These two functions do not directly give the height in this setup, but they show the triangle’s proportions. As the object rises, the angle increases. The values of sine, cosine, and tangent change in predictable ways, which lets students track vertical position over time with trigonometry.

Measuring Rocket Height with Trigonometry

measuring-rocket-height-with-trigonometry

radian and degree measure

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Trigonometric Wave Graphs and Asymptotes

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Trig Ratios for Right Triangle Sides

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trigonometric functions: problem solving

Measuring rocket height with trigonometry uses a fixed ground point and a changing angle of elevation. An observer stands a known horizontal distance from the launch site and watches the object rise. The angle between the ground and the line of sight gives the key information for finding height. The tangent function is the main tool for this calculation. Tangent is the ratio of the vertical side to the adjacent side in a right triangle. When the ground distance is fixed, the object’s height...

the law of sines

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...

the law of cosines

Using Cosines to Find Triangle Sides

The Law of Cosines helps find unknown sides and angles in any triangle. It is a key trig formula for non-right triangles, where the Pythagorean Theorem does not give a direct answer. The law links side lengths to the cosine of an angle, so students can solve triangles with missing measurements. For a triangle with sides a, b, and c and opposite angles A, B, and C, the formula is written as a squared equals b squared plus c squared minus 2bc cosine A. Similar equations can be used for the other...

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Unit Circle Trig Identities and Sum Formulas

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Double-Angle and Half-Angle Formulas

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Cofunction Identities and Complementary Angles

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Solving Trigonometric Equations

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key terms and concepts

Use tangent, sine, and cosine to measure a rocket’s height from a fixed ground point and track its rising angle with right-triangle trigonometry.

Measuring Rocket Height with Trigonometry | 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

Measuring Rocket Height with Trigonometry

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