Bearing Quiz

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What does 'Θ' represent in bearing terminology?

The direction of the observer

The distance from the object

The angle from the North-South line (correct)

The position of the object

In the notation 'N 30° E', what does it indicate?

The bearing is 30 degrees North towards the East direction (correct)

The angle is 30 degrees clockwise from the East

The direction is Southwest at 30 degrees

The angle is 30 degrees counterclockwise from the North

Which of the following describes the WE line in bearings?

It serves as the reference for angles measured from East.

It indicates distances rather than directions.

It runs horizontally at 90 degrees to the NS line. (correct)

It runs from South to North.

What does 'S 45° W' signify in terms of direction?

An angle of 45 degrees clockwise from the South towards the West Signup and view all the answers

Who is represented by 'O' in bearing notation?

The observer of the bearing Signup and view all the answers

What is the length of side AC in the right triangle?

60.95 m Signup and view all the answers

If angle B is 41 degrees and 50 minutes, what is the measure of angle A?

18 degrees and 10 minutes Signup and view all the answers

What is the total length (x) when combining side BC and side CD?

74.56 m Signup and view all the answers

How is the length of side BC calculated using tangent?

BC = tan(41° 50') * 60.95 Signup and view all the answers

What is the measure of angle C in the triangle?

90 degrees Signup and view all the answers

What does tan 40° equal in the triangle ΔABE if BE is known to be 4?

4 tan 40° Signup and view all the answers

How is the length EC calculated in triangle ΔBCE?

EC = 3.36 / cos 20° Signup and view all the answers

In triangle ΔCDE, if the value of x is calculated using the equation sin 60° = x / 3.58, what is x?

3.58 sin 60° Signup and view all the answers

If the value of BE is 3.36 in ΔABE, what is the relationship established by the angle?

tan 40° = BE / 4 Signup and view all the answers

What is the approximate numerical value of x if calculated as x = 3.58 sin 60°?

3.1 Signup and view all the answers

What is the total distance traveled by the boat from the starting point?

109.3 miles Signup and view all the answers

What is the bearing from the starting point to the endpoint?

N31°08' W Signup and view all the answers

Which equation correctly represents the relationship used to find θ?

$tan θ = rac{95}{54}$ Signup and view all the answers

What is the first direction the boat travels before making the turn?

North 29°15' East Signup and view all the answers

What value is used to calculate 'C', the distance from the endpoint to the starting point?

$rac{95}{sin 60°23'}$ Signup and view all the answers

What is the measure of angle B in triangle ABC?

32°40' Signup and view all the answers

What is the length of side c in triangle ABC?

185.27 Signup and view all the answers

How far is the ladder from the wall when it is 24 feet long and leaning against it at an angle of 18°10'?

7.5 feet Signup and view all the answers

What trigonometric function relates side a and side b in triangle ABC?

tan Signup and view all the answers

What is the value of side a in triangle ABC?

155.97 Signup and view all the answers

What is the defining characteristic of a right triangle?

It has one angle that is a right angle. Signup and view all the answers

In a right triangle, if one angle is 90 degrees, what can be said about the two other angles?

They are both acute and complementary. Signup and view all the answers

Which trigonometric function represents the ratio of the opposite side to the hypotenuse?

sine Signup and view all the answers

In the equation $tan heta = \frac{opp}{adj}$, what does 'opp' refer to?

The length of the opposite side. Signup and view all the answers

What is the correct relationship expressed by the cosine function?

It is the ratio of the adjacent side to the hypotenuse. Signup and view all the answers

Study Notes

Bearing Definition: Angle measured clockwise from the North-South line to an object sighted.
Bearings Notation: Expressed in the format of cardinal directions (e.g., N 30° E, S 45° W).
Bearings Calculation: Involves solving triangles using trigonometric functions to determine distances and angles.

Example Calculations

Triangle Properties:
- Right triangle with angles A (18° 10'), B (41° 50'), and C (90°).
- Side lengths: AC = 60.95m, CD = 20m, BC = 54.56m.
Trigonometric Relationships:
- ( tan(18° 10') = 20/AC ) leads to calculating AC.
- ( tan(41° 50') = BC/60.95 ) provides BC length through angle relations.

Boat Journey: Travels N29°15' E for 54 miles, then N60°45' W for 95 miles.
Final Computation:
- Total distance from starting point: C = 109.3 miles.
- Final bearing calculated as N31°08' W using trigonometric identities.

Angle of Elevation and Depression

Observer and Object Definition: E for eye level of the observer, O for the object sighted.
Calculation Tables: Use tangent and cosine relations for different triangles (ΔABE, ΔBCE, ΔCDE) to find side lengths.

Right Triangle ABC

Triangle Information: C = 90°, C = 57°20', side b = 100.
Angle B Calculation: B = 90° - 57°20' = 32°40'.
Side Length Calculation:
- Using cos(C) to find side c.
- Using tan(C) for side a, deriving lengths as c = 185.27 and a = 155.97.

Ladder Problem

Problem Setup: A 24-foot ladder leaning against a wall.
Distance Calculation: Using ( sin(18°10') = x/24 ), leads to x = 7.5 feet, determining horizontal distance from wall.

Basic Properties of Right Triangles

Right Triangle Characteristics: Contains one 90° angle; other angles must be acute and complementary.
Vertices and Angles: Labeled as A, B, C with opposite sides represented as a, b, c.

Trigonometric Functions

Definitions:
- ( sin \theta = \frac{opp}{hyp} )
- ( cos \theta = \frac{adj}{hyp} )
- ( tan \theta = \frac{opp}{adj} )
Importance: Key functions for calculating sides and angles in right triangles.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Description

Test your understanding of bearings and directions in navigation. This quiz covers the concept of bearings from an observer's point of view, including the notation and angle measurements associated with different bearings. Perfect for students studying navigation or geography!