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

人はロケットから一定の距離に立って、垂直打ち上げの準備をしています。ロケットが上方に移動すると、その位置と仰角は飛行中に連続的に変化します。三角関数は、この変化する角度をロケットの垂直高さ、絶対距離、および地面距離に結び付けます。接線関数は、ロケットの垂直高さを観測角度と固定された地面距離に関連付けます。ロケットの高さは、既知の地上距離に測定された角度の接線を掛けることによって求められます。角度の正弦はロケットの垂直高さと絶対距離の比を示し、余弦は地上距離と絶対距離の比を示します。垂直方向の高さがわかると、正弦波は高さを使用して絶対距離を計算でき、余弦波は地上距離を使用して同じことを行うことができます。角度が大きくなると、これらの三角関数関係は、計算された高さとロケットまでの観測距離の両方に影響します。これらの関数を適用することで、観測者は測定角度からのロケットの高さ、絶対距離、および地面距離を三角測量できます。

三角関数：問題解決

Trigonometric Functions: Problem Solving

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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

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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Unit Circle Trig: Signs and Symmetry

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Trigonometric Wave Graphs and Asymptotes

Trigonometric functions create repeating waves and curved graphs with clear symmetry. Their shapes come from the unit circle, where a point moves counterclockwise and its vertical and horizontal positions form the sine and cosine values. Sine and cosine graphs are smooth waves with the same period, or repeat length. Their ranges stay bounded between -1 and 1. Sine, cosine, and the other trig functions all show regular patterns, but each one has its own graph shape. Tangent is the ratio of...

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Trig Ratios for Right Triangle Sides

Right triangle trigonometry uses sine, cosine, and tangent to connect an acute angle with the sides of the triangle. These trig ratios describe how side lengths relate to one another in right-angled geometry. They give a clear way to measure the links between angles and sides. Sine compares the side opposite an angle to the hypotenuse. Cosine compares the side adjacent to the angle to the hypotenuse. Tangent compares the opposite side to the adjacent side. Each ratio depends on the angle, not...

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...

trigonometric identities i

Unit Circle Trig Identities and Sum Formulas

Trigonometric identities link trigonometric functions and stay true for every angle in their domains. A key example is the Pythagorean identity, which comes directly from the geometry of the unit circle. For an angle θ, a point on the unit circle has coordinates (cos θ, sin θ). Because the radius is 1, the Pythagorean Theorem gives the basic identity. That same identity can be rearranged to create another useful form. If it is divided by cos²θ, assuming cos θ is not 0, it leads to a second...

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Double-Angle and Half-Angle Formulas

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Cofunction Identities and Complementary Angles

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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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