Podcast
Questions and Answers
What is the true bearing of a direction that is 45 degrees east of north?
What is the true bearing of a direction that is 45 degrees east of north?
- 315 degrees
- 135 degrees
- 045 degrees (correct)
- 225 degrees
If a triangle has angles of 30 degrees and 60 degrees, what is the measure of the third angle?
If a triangle has angles of 30 degrees and 60 degrees, what is the measure of the third angle?
- 120 degrees
- 30 degrees
- 90 degrees (correct)
- 60 degrees
Which of the following statements about compass bearings is true?
Which of the following statements about compass bearings is true?
- True bearings and compass bearings are identical.
- Compass bearings are always measured in degrees from south.
- Compass bearings are measured clockwise from north. (correct)
- Compass bearings can only be expressed in whole numbers.
In a right triangle, if one angle measures 45 degrees, what is the measure of the other acute angle?
In a right triangle, if one angle measures 45 degrees, what is the measure of the other acute angle?
Which of the following is a method for calculating the length of a side in a right triangle?
Which of the following is a method for calculating the length of a side in a right triangle?
Study Notes
Compass Bearings
- Compass bearings are expressed in terms of cardinal directions: North, South, East, and West.
- Bearings are typically measured clockwise from the North direction.
- A bearing is written as a three-figure number, such as 045° for 45 degrees east of North.
True Bearings
- True bearings use a 360° circle to specify directions, allowing for more precise navigation.
- They are measured clockwise from true North: 0° indicates North, 90° indicates East, 180° indicates South, and 270° indicates West.
- True bearings are essential in navigational contexts, like maritime or aerial navigation, to ensure accurate direction.
Trigonometry in Navigation
- Trigonometry is vital for solving problems involving angles and distances.
- The primary functions used are sine, cosine, and tangent, relating angles to ratios of sides in right triangles.
- The sine function (sin) links an angle to the ratio of the opposite side over the hypotenuse.
- The cosine function (cos) relates the angle to the ratio of the adjacent side over the hypotenuse.
- The tangent function (tan) connects the angle to the ratio of the opposite side over the adjacent side.
Finding Sides and Angles
- The Pythagorean theorem (a² + b² = c²) gives the relationship between the sides of a right triangle.
- To find an unknown angle in right triangles, apply the inverse trigonometric functions:
- sin⁻¹ for sine
- cos⁻¹ for cosine
- tan⁻¹ for tangent
- When working with non-right triangles, the Law of Sines and Law of Cosines can be used:
- Law of Sines: (a/sinA) = (b/sinB) = (c/sinC)
- Law of Cosines: c² = a² + b² - 2ab*cos(C)
Practical Applications
- Compass bearings and true bearings are used in various fields, including aviation, marine navigation, and land surveying.
- Understanding trigonometry helps in real-world applications, such as construction, architecture, and navigation.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
This practice test focuses on compass bearings, true bearings, and calculating sides and angles through trigonometry. Sharpen your skills in navigation and geometry with a series of questions designed to enhance your understanding of these essential concepts.
