Sin Cos and Tan - Basic Trigonometry Example

TL;DR

Learn how to use trigonometry to calculate the height and length of a roof with given measurements and angles.

Transcript

okay for the example of trigonometry I have here I'm going to be dealing with a roof okay um because it's a nice example which you may probably use in the future okay well this roof it spans 5,200 mm it also has these Eve overhangs on each side of 600 this roof has a pitch of 23° so the things which we're going to be wanting to find out with this r... Read More

Key Insights

• 🌍 Trigonometry can be applied to real-world scenarios, such as calculating roof dimensions.
• 🙃 Labeling the sides of the triangle is crucial for correctly applying trigonometric functions.
• ❓ The tangent function is used to determine the height of the roof, while the cosine function is used to find the length of the rafter.
• 🔺 Additional angles in a triangle can be found by subtracting known angles from 180°.
• 👷 Understanding trigonometry can help in various construction and engineering projects.
• ❓ Trigonometric calculations require a scientific calculator for accurate results.
• 🆘 The provided example helps to enhance understanding of trigonometry concepts.

Questions & Answers

Q: How can trigonometry be used to calculate the height of a roof?

To calculate the height of a roof, you can create a triangle using the given measurements and angles. By applying the tangent function, you can find the height by dividing the opposite side (roof length) by the adjacent side (600 mm). The final calculation will give you the height of the roof.

Q: What is the process for calculating the length of a rafter using trigonometry?

To calculate the rafter length, you need to create another triangle using the given measurements and angles. This time, you will use the cosine function, as you have the adjacent side (3,200 mm) and the hypotenuse (unknown rafter length). By substituting the values and solving the equation, you can find the length of the rafter.

Q: How can we determine the angle of a triangle given other angle measurements?

To find an additional angle in the triangle, you can use the fact that the sum of all angles in a triangle is 180°. By subtracting the known angles (90° and 23°) from 180°, you can calculate the third angle. In the provided example, the angle was found to be 67°.

Q: What is the key concept behind using trigonometry in real-world applications?

The key concept is to utilize trigonometric functions to relate angles and side lengths in a right triangle. By appropriately labeling the sides, choosing the correct function, and substituting values, you can calculate unknown measurements accurately.

Summary & Key Takeaways

• The content discusses using trigonometry to calculate the height and length of a roof with specific measurements and angles.

• It explains how to label the sides of the triangle, determine the appropriate trigonometric function (sine, cosine, or tangent), substitute in values, and calculate the unknown variables.

• The video also briefly mentions finding an additional angle in the triangle as well.