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Tarzan grabs a vine, which is initially horizontal, and attempts to swing to the ground. Tarzan weighs 890 N and the breaking strength of the vine he knows is 1780 N. A Tarzan swings he is surprised to find that the vine breaks at a certain angle theta. Find theta.

Tarzan grabs a vine, which is initially horizontal, and attempts to swing to the ground. Tarzan weighs 890 N and the breaking strength of the vine he knows is 1780 N. A Tarzan swings he is surprised to find that the vine breaks at a certain angle theta. Find theta.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
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Tarzan grabs a vine, which is initially horizontal, and attempts to swing to the ground. Tarzan weighs 890 N and the breaking strength of the vine he knows is 1780 N. A Tarzan swings he is surprised to find that the vine breaks at a certain angle theta. Find theta. 

The image depicts a right triangle used to illustrate a physics or trigonometry problem involving angles and distance. Here is a detailed explanation of the diagram and its components: 1. **Overview of the Diagram:** - The diagram features a right triangle labeled with various notation and depiction of human figures for contextual understanding of the problem. 2. **Key Elements of the Diagram:** - At the top left of the triangle, there is a depiction of a tree or a structure with a stick figure standing on a platform. - The hypotenuse of the triangle is represented with an arrow starting from the top right corner and going down to the bottom left, which could signify a distance (denoted as 'l'). - The right angle is indicated at the bottom left corner of the triangle. - The point at the bottom left (near the right angle) shows another stick figure, this could indicate the point of observation or measurement. - The label ‘Asinθ’ appears on the side opposite to the angle θ, which signifies the length of this side in terms of the angle θ. 3. **Mathematical Notations:** - **θ (theta):** This angle is located at the top right corner of the triangle. This is the angle of elevation from the observer (bottom left) to the stick figure standing at the right end of the hypotenuse. - **l (small 'ell'):** This appears to be the length of the hypotenuse of the triangle. 4. **Purpose and Application:** - The diagram aims to calculate the opposite side of the right triangle using a trigonometric function, with Asinθ indicating the calculation involving the sine function. Specifically, the sine function is being used to determine the length of the side opposite to angle θ from the hypotenuse length ‘l’. - This could be applied to real-world problems involving height and distance estimation, such as measuring the height of a structure using trigonometric principles. This annotated diagram aids in visualizing how trigonometric functions are applied to solve problems involving right-angled triangles.
Transcribed Image Text:The image depicts a right triangle used to illustrate a physics or trigonometry problem involving angles and distance. Here is a detailed explanation of the diagram and its components: 1. **Overview of the Diagram:** - The diagram features a right triangle labeled with various notation and depiction of human figures for contextual understanding of the problem. 2. **Key Elements of the Diagram:** - At the top left of the triangle, there is a depiction of a tree or a structure with a stick figure standing on a platform. - The hypotenuse of the triangle is represented with an arrow starting from the top right corner and going down to the bottom left, which could signify a distance (denoted as 'l'). - The right angle is indicated at the bottom left corner of the triangle. - The point at the bottom left (near the right angle) shows another stick figure, this could indicate the point of observation or measurement. - The label ‘Asinθ’ appears on the side opposite to the angle θ, which signifies the length of this side in terms of the angle θ. 3. **Mathematical Notations:** - **θ (theta):** This angle is located at the top right corner of the triangle. This is the angle of elevation from the observer (bottom left) to the stick figure standing at the right end of the hypotenuse. - **l (small 'ell'):** This appears to be the length of the hypotenuse of the triangle. 4. **Purpose and Application:** - The diagram aims to calculate the opposite side of the right triangle using a trigonometric function, with Asinθ indicating the calculation involving the sine function. Specifically, the sine function is being used to determine the length of the side opposite to angle θ from the hypotenuse length ‘l’. - This could be applied to real-world problems involving height and distance estimation, such as measuring the height of a structure using trigonometric principles. This annotated diagram aids in visualizing how trigonometric functions are applied to solve problems involving right-angled triangles.
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