17 Trigonometry Compass Directions N S N S N 45° E 45° E W E W 30°

Slides:

Advertisements

Similar presentations

TANGENT RATIO CHAPTER 7 Section 4 Jim Smith JCHS.

Advertisements

Get a calculator!  How many parts are there to a triangle ? a b c  C Pardekooper AA BB CC.

8 – 5 The Tangent Ratio.

Trigonometry Solving Triangles ADJ OPP HYP  Two old angels Skipped over heaven Carrying a harp Solving Triangles.

Unit 35 Trigonometric Problems Presentation 1Finding Angles in Right Angled Triangles Presentation 3Problems using Trigonometry 2 Presentation 4Sine Rule.

Trigonometric ratios.

TRIGONOMETRY. Sign for sin , cos  and tan  Quadrant I 0° <  < 90° Quadrant II 90 ° <  < 180° Quadrant III 180° <  < 270° Quadrant IV 270 ° < 

Y10 Triangle Starters Pythagoras APythagoras A | Pythagoras A AnswersPythagoras A Answers Pythagoras BPythagoras B | Pythagoras B AnswersPythagoras B Answers.

60º 5 ? 45º 8 ? Recall: How do we find “?”. 65º 5 ? What about this one?

Math 416 Trigonometry.

Learning how to … use Pythagoras’ Theorem to calculate a shorter side of a right-angled triangle Mathematics GCSE Topic Reminders.

Engineering Fundamentals Session 6 (1.5 hours). Trigonometry Triangle: –Geometric figure with 3 straight sides and 3 angles. Sides Angles.

SECTION 8.4 TRIGONOMETRY. The word trigonometry comes from two greek terms, trigon, meaning triangle, and metron, meaning measure. a trigonometric ratio.

Trigonometry Supplemental Questions. Problem 1 Jessica observed a mountain climber reaching the summit, which is known to be at 2,358 ft. If Jessica is.

VECTORS IN MECHANICS.

Trig Review: PRE-AP Trigonometry Review Remember right triangles? hypotenuse θ Opposite side Adjacent side Triangles with a 90º angle.

Classifying Triangles By Angles Acute: all three angles are less than 90 ◦ Obtuse: one angle is greater than 90 ◦ Right: one angle measure is 90 ◦ By.

CHAPTER 8 RIGHT TRIANGLES

INVERSE TANGENT GEO200 tan = opposite adjacent  = tan -1 opposite adjacent INVERSE TANGENT: (tan -1 ) finds the measure of the angle of a right triangle.

Section 1 – Trigonometry and the Graphing Calculator After this section, you should be able to show that you can: Know the SIX trig. functions Change degree-minutes.

Triangle Author: Kit Date: Introduction In this slide show, we will talk about the right triangle and some properties Pythagoras’ Theorem.

Trigonometry Revision. B AC 30 º hypotenuse adjacent opposite.

Chapter 9 - Trigonometry. Trigonometry: tri’gonon - triangle met’ron - measure.

World 5-1 Trigonometric Ratios. Recall that in the past finding an unknown side of a right triangle required the use of Pythagoras theorem. By using trig.

Pythagoras Theorem Example For each of the following right angled triangles find the length of the lettered side, giving your answers to 2 decimal places.

Trigonometry. Starter 10 cm cm cm cm cm.

TRIGONOMETRY Lesson 2: Solving Right Triangles. Todays Objectives Students will be able to develop and apply the primary trigonometric ratios (sine, cosine,

Trigonometry Pythagoras Theorem & Trigo Ratios of Acute Angles.

Trigonometry 2 Finding the angle when the sides are given.

TRIGONOMETRY – Functions 1 We will now place the angle in the x–y plane. The initial side of the angle will always be placed on the (+) side of the x –

Chapter 8: Right Triangles & Trigonometry 8.3 The Tangent Ratio.

Each group starts with £50 Each round, you must decide which question you will answer (£10, £15 or £20) – the higher the stake, the harder the question.

A Quick Review ► We already know two methods for calculating unknown sides in triangles. ► We are now going to learn a 3 rd, that will also allow us to.

8-5 The Tangent Ratio.  Greek for “Triangle Measurement”  You will need to use a scientific calculator to solve some of the problems. (You can find.

Copyright © 2013, 2009, 2005 Pearson Education, Inc. 1 2 Acute Angles and Right Triangles.

Lesson 8-5 The Tangent Ratio (page 305) How can trigonometric ratios be used to find sides and angles of a triangle?

© T Madas. A bearing is a way of defining direction as an angle measured from due North in a clockwise direction N A B 063° In other words if you are.

14-3 Right Triangle Trig Hubarth Algebra II. The trigonometric ratios for a right triangle: A B C a b c.

8-2 Trigonometric Ratios Warm Up Lesson Presentation Lesson Quiz

2 Acute Angles and Right Triangles.

Chapter 17: Trigonometry

Trigonometric Identities II Double Angles.

3-Dimensional Pythagoras & Trigonometry

Grade 10 Academic (MPM2D) Unit 5: Trigonometry Introduction to Trigonometry Mr. Choi © 2017 E. Choi – MPM2D - All Rights Reserved.

Copyright © 2017, 2013, 2009 Pearson Education, Inc.

Basic Trigonometry We will be covering Trigonometry only as it pertains to the right triangle: Basic Trig functions:  Hypotenuse (H) Opposite (O) Adjacent.

Trigonometric Identities III Half Angles or t-formulae.

Pythagoras’ Theorem and Trigonometry

Angles of Elevation and Depression

Using the Pythagoras Theorem.

Geometry Lesson 8 – 4 Trigonometry Objective:

7.4 - The Primary Trigonometric Ratios

Triangle Starters Pythagoras A | Answers Pythagoras B | B Answers

9.5 The Sine & Cosine Ratios

Objective Use trigonometric ratios to find angle measures in right triangles and to solve real-world problems.

Y10 Triangle Starters Pythagoras A | Pythagoras A Answers

2a Basic Trigonometric Functions Sine, Cosine, and tangent

Bearings s.small.

Trigonometry Monday, 18 February 2019.

©G Dear2008 – Not to be sold/Free to use

9.5 The Sine & Cosine Ratios

Pythagoras Theorem Example

Trigonometry (Continued).

Pythagoras's Theorem Tuesday, 21 May 2019.

Trigonometric Ratios Geometry.

Unit III Trigonometric Ratios Holt Geometry.

Reviewing Trig Ratios 7.4 Chapter 7 Measurement 7.4.1

Trigonometry: Answers to 1dp Trigonometry: Answers to 1dp 1.) 2.) b

Maths Unit 23 – Pythagoras & Trigonometry

Presentation transcript:

17 Trigonometry Compass Directions N S N S N 45° E 45° E W E W 30° E 30° S N S N S W 60° N 60° E W E W 20° S 20° W

17 Trigonometry Compass Directions N B W E 6 km 4 km N S C W E A S A ship leaves a port A and sails a distance of 4 km in the direction N 30° E to a point B. The ship then changes direction and sails for a further 6 km in the direction S 60° E to a point C. (i) Calculate the distance from the ship’s present position at point C to port A. (ii) Find |∠BCA|, to the nearest degree. (iii) Hence, find the direction of C from A. N S E W 30° B 60° 6 km 4 km N S E W 30° C A

17 Trigonometry Compass Directions B 6 km 4 km C A (i) Calculate the distance from the ship’s present position at point C to port A. 4 km 6 km 90° C A B |AC|2 = 42+62 (Theorem of Pythagoras) |AC|2 = 16+36 |AC|2 = 52 |AC| = 52 ∴ |AC| = 7.2 km, to 1 decimal place

17 Trigonometry Compass Directions B Adjacent Opposite 4 km 6 km C A (ii) Find |∠BCA|, to the nearest degree. 4 km 6 km 90° C A B Opposite Adjacent 𝜽° tan 𝜃= 4 6 𝜃=ta n −1 4 6 𝜃=33.69006…°   ∴ |∠BCA| = 34°, to nearest degree

17 Trigonometry Compass Directions B 6 km N 4 km N W E C W E A 4° S S (iii) Find the direction of C from A. N S E W 30° 60° A C 4 km 6 km B 30° N S W E 34° 30° 34°− 30° =4° 4° Hence, the direction of C from A is E 4° N.