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

Une personne se tient à une distance fixe d’une fusée, se préparant à un lancement vertical.Au fur et à mesure que la fusée se déplace vers le haut, sa position et son angle d’élévation changent continuellement pendant le vol.Les fonctions trigonométriques lient cet angle changeant à la hauteur verticale, à la distance absolue et à la distance au sol de la fusée.La fonction tangente relie la hauteur verticale de la fusée à l’angle observé et à la distance fixe au sol.La hauteur de la fusée est déterminée en multipliant la distance au sol connue par la tangente de l’angle mesuré.Le sinus de l’angle donne le rapport entre la hauteur verticale de la fusée et la distance absolue, tandis que le cosinus donne le rapport entre la distance au sol et la distance absolue.Une fois que la hauteur verticale est connue, le sinus peut calculer la distance absolue à l’aide de la hauteur, et le cosinus peut faire de même en utilisant la distance au sol.Au fur et à mesure que l’angle augmente, ces relations trigonométriques affectent à la fois la hauteur calculée et la distance observée par rapport à la fusée.En appliquant ces fonctions, les observateurs peuvent trianguler la hauteur de la fusée, la distance absolue et la distance au sol par rapport à l’angle mesuré.

fonctions trigonométriques : résolution de problèmes

Trigonometric Functions: Problem Solving

Lors de l&#8217;observation de l&#8217;ascension verticale d&#8217;un objet depuis une position fixe au sol, comme lors du lancement d&#8217;une fus&#233;e, les relations trigonom&#233;triques offrent une m&#233;thode pr&#233;cise pour d&#233;terminer la hauteur de l&#8217;objet. &#192; mesure que l&#8217;objet s&#8217;&#233;l&#232;ve, un observateur plac&#233; &#224; une distance horizontale connue du site de lancement mesure l&#8217;angle form&#233; entre le sol et la ligne reliant sa position &#224; la position actuelle de l&#8217;objet. Cet angle d&#8217;&#233;l&#233;vation fournit des informations essentielles reliant la position observ&#233;e &#224; la hauteur au-dessus du sol.
La fonction tangente joue un r&#244;le central dans cette analyse. D&#233;finie comme le rapport entre le c&#244;t&#233; oppos&#233; et le c&#244;t&#233; adjacent dans un triangle rectangle, elle permet de calculer la hauteur lorsque la distance horizontale est fix&#233;e. Plus pr&#233;cis&#233;ment, la hauteur de l&#8217;objet s&#8217;obtient en multipliant la distance horizontale s&#233;parant l&#8217;observateur du point de lancement par la tangente de l&#8217;angle mesur&#233; entre le sol et la ligne de vis&#233;e de l&#8217;objet.
Les fonctions sinus et cosinus apportent des informations compl&#233;mentaires. Le sinus de l&#8217;angle repr&#233;sente le rapport entre la hauteur de l&#8217;objet et la distance oblique le long de la ligne de vis&#233;e (l&#8217;hypot&#233;nuse), tandis que le cosinus relie la distance horizontale &#224; cette m&#234;me distance oblique. Bien que ces deux fonctions ne soient pas utilis&#233;es directement pour calculer la hauteur, elles d&#233;crivent les proportions g&#233;om&#233;triques du triangle form&#233; par le sol, la hauteur verticale et la ligne de vis&#233;e.
&#192; mesure que l&#8217;angle d&#8217;&#233;l&#233;vation augmente durant l&#8217;ascension de l&#8217;objet, les valeurs de ces fonctions trigonom&#233;triques &#233;voluent de mani&#232;re pr&#233;visible, offrant un cadre math&#233;matique permettant de suivre avec pr&#233;cision la position verticale de l&#8217;objet au fil du temps.

Fonctions trigonométriques : résolution de problèmes

Lors de l&#8217;observation de l&#8217;ascension verticale d&#8217;un objet depuis une position fixe au sol, comme lors du lancement d&#8217;une ...

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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

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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...

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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.

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Measuring Rocket Height with Trigonometry

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