Finding trig functions of special angles example | Trigonometry | Khan Academy | Summary and Q&A

TL;DR

This video explains how to solve an isosceles triangle using the given side lengths and angle measures.

Key Insights

• 🔺 The given triangle in the video is an isosceles triangle because it has two sides with the same length.
• 🔺 The base angles of an isosceles triangle are congruent.
• 🔺 The measure of the angle opposite the two equal sides in an isosceles triangle can be determined using the sum of interior angles.
• 🙃 In an isosceles triangle, the unknown side lengths can be found using the properties of congruent sides.
• 🔺 The triangle in the video is also an equilateral triangle because all angles have the same measure.
• 🤨 The angle measures in radians in the triangle are pi over six, pi over three, and pi over two.
• 🗯️ The Pythagorean Theorem can be used to find the length of the unknown side in a right triangle.

Transcript

Voiceover:The first thing I want to do in this video is given the information given about this triangle. Figuring out the unknowns, figuring out the length here this value a, figuring out this length in orange, b, figuring out the measure of this angle which we'll call alpha in figuring out in radians and figuring out the measure of this angle, rig... Read More

Questions & Answers

Q: How can you determine if a triangle is isosceles?

A triangle is isosceles if it has two sides that have the same length. In the video, it is determined that the triangle is isosceles because two sides have a length of two units.

Q: How are the base angles of an isosceles triangle related?

In an isosceles triangle, the base angles are congruent. This means that if one base angle is pi over three radians, the other base angle will also be pi over three radians.

Q: How can you find the measure of an angle in an isosceles triangle?

By using the sum of interior angles in a triangle, you can determine the measure of an angle. In the video, it is shown that the angle opposite the two equal sides is pi over six radians.

Q: How can you find the unknown side lengths in an isosceles triangle?

If you know the length of one side in an isosceles triangle, you can conclude that the other equal side has the same length. In the video, it is determined that the unknown side length is equal to one unit.

Summary & Key Takeaways

• The video explains how to solve for the unknown side lengths and angle measures in an isosceles triangle.

• It is determined that the triangle in the video is an isosceles triangle because two sides have the same length.

• By using the properties of isosceles triangles and the sum of interior angles, the measures of the unknown angles and side lengths are determined.