Applying angle addition formula for sin | Trig identities and examples | Trigonometry | Khan Academy

TL;DR

Using trigonometric functions and identities, we can find the length of a given segment in a right triangle.

Transcript

Voiceover:What I want to do in this video is use all of our powers, all of our knowledge of trig functions and trig identities. In order to figure out, given all the information that we have here, in order to figure out the length of this yellow line, this point, this line or the segment that goes from here to here. I encourage you to pause the vid... Read More

Key Insights

• 🗯️ Trigonometric functions and identities can be used to solve problems involving right triangles.
• 👨‍💼 The sine of a combined angle can be expressed using the sine and cosine of the individual angles.
• 👨‍💼 The values for sine and cosine can be determined based on the definitions of these functions.
• 🔺 Finding the length of a segment in a right triangle involves considering the combined angle formed by two given angles.

Questions & Answers

Q: How can the length of a segment in a right triangle be found?

By considering the combined angle formed by two given angles, the trigonometric function sine can be used to find the length of the segment.

Q: What is the expression for sine of the combined angle?

The sine of the combined angle, alpha plus beta, can be expressed as the product of the sine of alpha times the cosine of beta, plus the cosine of alpha times the sine of beta.

Q: How can the values of sine and cosine for the individual angles be determined?

By using the definitions of sine and cosine, the values for sine of alpha, cosine of beta, cosine of alpha, and sine of beta can be calculated based on the given information in the right triangle.

Q: What is the final answer for the length of the segment?

The length of the segment is equal to three plus four square roots of three, divided by ten.

Summary & Key Takeaways

• The video explains how to find the length of a segment in a right triangle by considering the combined angle of two given angles.

• By using the trigonometric function sine, the length of the segment can be determined.

• Trigonometric identities can be used to express the sine of the combined angle in terms of the sines and cosines of the individual angles involved.