Using tangent to find the missing length of a triangle
Summary
TLDRIn this video, the instructor explains how to work with right triangles, focusing on identifying the hypotenuse, adjacent, and opposite sides based on a given angle. The video emphasizes the use of trigonometric functions, particularly the tangent function, to find unknown side lengths. The instructor provides a step-by-step example using a 52° angle and an adjacent side length of 13 to calculate the opposite side length. The importance of ensuring the calculator is in degree mode is also highlighted.
Takeaways
- 📐 Identify the hypotenuse as the side opposite the right angle.
- 📝 The adjacent side connects the angle to the right angle.
- 🔄 The opposite side is directly across from the angle.
- 📊 Use sine, cosine, and tangent for calculations.
- 📏 Tangent = opposite / adjacent.
- 🔍 For a given angle, set up the tangent equation to find unknowns.
- 🧮 Ensure your calculator is in degree mode before calculations.
- 🔗 Use known side lengths to solve for unknowns.
Timeline
- 00:00:00 - 00:03:39
In this segment, the speaker explains the components of a right triangle, focusing on identifying the hypotenuse, adjacent side, and opposite side relative to a given angle. The hypotenuse is defined as the side opposite the right angle, while the adjacent side connects the angle to the right angle, and the opposite side is directly across from the angle. The speaker emphasizes the use of trigonometric functions (sine, cosine, and tangent) to find unknown side lengths, particularly when the triangle does not conform to special right triangle ratios. Given an angle of 52° and the adjacent side length of 13, the speaker decides to use the tangent function to solve for the opposite side, leading to the equation tangent(52°) = x/13. After rearranging and calculating, the speaker finds the value of the opposite side to be approximately 16.64.
Mind Map
Video Q&A
What is the hypotenuse in a right triangle?
The hypotenuse is the side directly across from the right angle.
How do you identify the adjacent side?
The adjacent side connects the given angle and the right angle.
What is the opposite side?
The opposite side is directly across from the given angle.
Which trigonometric functions are used for right triangles?
The sine, cosine, and tangent functions are used.
How do you calculate the tangent of an angle?
The tangent of an angle is equal to the ratio of the opposite side to the adjacent side.
What should you check before using a calculator for trigonometric functions?
Ensure your calculator is in degree mode.
How do you solve for an unknown side using tangent?
Set up the equation using the tangent function and solve for the unknown side.
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- right triangle
- hypotenuse
- adjacent side
- opposite side
- trigonometric functions
- tangent
- sine
- cosine
- angle
- calculator