Trigonometry: Angle of Elevation Word Problem - Find the Length of the Shadow | Summary and Q&A

TL;DR
The video demonstrates how to find the length of a shadow using the angle of elevation of the sun and the height of an object, through the use of trigonometry.
Key Insights
- 😎 The length of a shadow cast by an object can be calculated using the angle of elevation of the sun and the height of the object, through trigonometric principles.
- 👨💼 Trigonometric functions such as sine, cosine, and tangent are useful for solving problems related to the length of shadows and angles of elevation or depression.
- 🙃 The tangent function (tan) can be particularly helpful in finding the length of a shadow, as it relates the opposite and adjacent sides of a right triangle.
- 😫 It is important to ensure that calculators are set to the correct units (degrees) when performing trigonometric calculations.
Transcript
Read and summarize the transcript of this video on Glasp Reader (beta).
Questions & Answers
Q: How can you calculate the length of a shadow using the angle of elevation of the sun?
To calculate the length of a shadow, you need to use trigonometry. By knowing the angle of elevation of the sun and the height of the object, you can apply the tangent function to find the length of the shadow.
Q: What is the significance of the angle of elevation in shadow calculations?
The angle of elevation of the sun is crucial in shadow calculations because it determines the inclination of the sun's rays. This angle, combined with the height of the object, allows us to calculate the length of the shadow.
Q: What are the trigonometric functions used in finding the length of a shadow?
In this scenario, the video uses the tangent function (tan) to calculate the length of the shadow. By using the formula tan(theta) = opposite/adjacent, we can solve for x (the length of the shadow).
Q: Can this method be used for objects of any height?
Yes, this method can be used for objects of any height. As long as you know the angle of elevation of the sun and the height of the object, you can use trigonometry to calculate the length of the shadow.
Summary & Key Takeaways
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The video explains how to use trigonometry to calculate the length of a shadow cast by an object, given the angle of elevation of the sun and the height of the object.
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It demonstrates the process through the use of a diagram and a triangle, where the angle of elevation is known and the length of the shadow is unknown.
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By applying the tangent function and solving for the unknown variable, the video concludes that the length of the shadow is approximately 13.3 feet when the angle of elevation is 23.4 degrees.
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