Angle of sun with the ground based on shadow | Trigonometry | Khan Academy

TL;DR

In this video, the angle of the sun's rays hitting the ground is calculated using trigonometry.

Transcript

Voiceover:We have this girl right over here and she is 1.7 meters tall and she's standing in the sun. The sun's at an angle with respect to the ground. Given where the sun is right now, her shadow is 3.1 meters long. What I want you to do is pause this video and try to figure that angle of the sun relative to the ground or another way, let me be a ... Read More

Key Insights

• 🔺 Trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles.
• 🙃 The tangent function is used to calculate angles when the opposite and adjacent sides are known.
• 🥳 Inverse tangent, or the arctangent function, is used to find the angle when the tangent ratio is known.
• 😎 Calculating the angle of the sun's rays using trigonometry can have practical applications in various fields.
• 📐 Radians are a unit of measurement commonly used in mathematics and physics for angular measurements.
• 🌍 Trigonometry can help in understanding and predicting the behavior of angles and distances in real-world scenarios.
• 👨‍💼 Trigonometric functions like sine, cosine, and tangent are fundamental tools used in many scientific and engineering calculations.

Questions & Answers

Q: How is the angle of the sun's rays calculated using trigonometry?

The tangent function is used by taking the ratio of the girl's height (opposite side) to the length of her shadow (adjacent side). The inverse tangent of this ratio gives the angle in radians.

Q: Why is the tangent function used instead of other trigonometric functions?

The tangent function deals with the ratios of the opposite and adjacent sides, which is what we have in this situation with the girl's height and the length of her shadow.

Q: What is the significance of calculating the angle of the sun's rays?

Calculating the angle helps in understanding the direction and intensity of the sun's rays, which can have various implications in fields such as architecture, photography, and solar energy.

Q: What is the unit of measurement used for the angle in this calculation?

The angle is measured in radians, which is a unit of angular measurement commonly used in mathematics and physics.

Summary & Key Takeaways

• A girl standing in the sun casts a shadow that is 3.1 meters long, and her height is 1.7 meters.

• By using the tangent function, the angle of the sun's rays relative to the ground can be calculated as approximately 0.50 radians.

• Trigonometry is used to determine the angle by considering the opposite and adjacent sides of a right triangle formed by the girl's height, the length of her shadow, and the angle of the sun.