Q1, ACT Compass Trigonometry (official sample test problems)

TL;DR

Learn how to find the length of a segment in a right triangle using trigonometric functions such as sine, cosine, and tangent.

Transcript

for the first question we are given this red triangle and we know that the length of a B is 8 and then the angle measure for angle a is 60 degrees and right here he also tells us about the sine of 60 degrees cosine 60 degrees and also tangent 60 degrees values right but then the question is asking us approximately how many units long is the segment... Read More

Key Insights

• 🗯️ The length of a segment in a right triangle can be found using trigonometric functions such as sine, cosine, and tangent.
• 👨‍💼 The sine function relates the opposite side to the hypotenuse, while the cosine function relates the adjacent side to the hypotenuse.
• 🗯️ The tangent function relates the opposite side to the adjacent side in a right triangle.
• 😫 By setting up the appropriate trigonometric equation and solving, the length of a segment can be determined.
• 💼 In this case, the sine function was used to find the length of segment BC in the given right triangle.
• 💁 The angle and side length provided were used to form the equation, which was then simplified and solved to find the length of BC.
• 🇦🇪 The value obtained was approximately 6.93 units.

Questions & Answers

Q: How can we find the length of segment BC in the given right triangle?

The length of segment BC can be found using the sine function and setting up the ratio of the opposite side to the hypotenuse. By multiplying both sides of the equation by the hypotenuse, the length can be calculated.

Q: What is the value of angle a in the right triangle?

The value of angle a in the right triangle is given as 60 degrees.

Q: What are the other trigonometric functions mentioned in the video?

The video mentions cosine and tangent as other trigonometric functions. Cosine is the ratio of the adjacent side to the hypotenuse, while tangent is the ratio of the opposite side to the adjacent side.

Q: How was the length of BC approximated to 6.93 units?

By substituting the given values into the equation and solving, the length of BC was found to be approximately 6.93 units.

Summary & Key Takeaways

• Given a red triangle with an angle of 60 degrees and a side length of 8, the question asks for the approximate length of the segment BC.

• The video explains how to use the sine function to find the length of BC by setting up the ratio of the opposite side to the hypotenuse.

• By multiplying both sides of the equation by 8 and solving, the length of BC is found to be approximately 6.93 units.