Example 1 : Find the area of the triangle ABC.

Slides:



Advertisements
Similar presentations
Powerpoint hosted on Please visit for 100’s more free powerpoints.
Advertisements

The Sine Rule. A B C ao bo co.
5-May-15 Exact Values Angles greater than 90 o Trigonometry Useful Notation & Area of a triangle Using Area of Triangle Formula Cosine Rule Problems Sine.
Trigonometry Solving Triangles ADJ OPP HYP  Two old angels Skipped over heaven Carrying a harp Solving Triangles.
Solution of Triangles SINE RULE. 22 angle dan 1 side are given e.g  A = 60 ,  B = 40  and side b = 8 cm then, side a & side c can be found using.
EXAMPLE 1 Solve a triangle for the SAS case Solve ABC with a = 11, c = 14, and B = 34°. SOLUTION Use the law of cosines to find side length b. b 2 = a.
Using Trigonometry to find area of a triangle The area of a triangle is one half the product of the lengths of two sides and sine of the included angle.
7-Aug-15Created by Mr. Lafferty Maths Dept. Exact Values Angles greater than 90 o Trigonometry Useful Notation & Area of a triangle.
13-5 The Law of Sines Warm Up Lesson Presentation Lesson Quiz
Trigonometry 2 Aims Solve oblique triangles using sin & cos laws Objectives Calculate angles and lengths of oblique triangles. Calculate angles and lengths.
Trigonometrical rules for finding sides and angles in triangles which are not right angled.
The sine rule When the triangles are not right-angled, we use the sine or cosine rule. Labelling triangle Angles are represented by upper cases and sides.
13-Aug-15Created by Mr. Lafferty Maths Dept. Trigonometry Cosine Rule Finding a Length Sine Rule Finding a length Mixed Problems.
8.3 Solving Right Triangles
The Area Of A Triangle. AoAo BoBo CoCo a b c. Finding The Formula. Consider the triangle below: AoAo BoBo CoCo a b c By drawing an altitude h we can calculate.
Similar Triangles and other Polygons
Chapter 14 Formulae. Learning Objectives Write expressions in algebra Write expressions in algebra Write a formula Write a formula Know the difference.
There are three ratios that you need to learn: Where are the hypotenuse, adjacent and opposite lengths. This is opposite the right-angle This is next to.
Pythagoras Theorem a2 + b2 = c2
9.5 Apply the Law of Sines day 3 How do you use the law of sines to find the area of a triangle?
Solution of Triangles COSINE RULE. Cosine Rule  2 sides and one included angle given. e.g. b = 10cm, c = 7 cm and  A = 55° or, a = 14cm, b = 10 cm and.
{ Law of Sines and Cosines Trigonometry applied to triangles without right angles. 1.
Lesson 6.1 Law of Sines. Draw any altitude from a vertex and label it k. Set up equivalent trig equations not involving k, using the fact that k is equal.
Trigonometry 2. Finding Sides Of Triangles. L Adj’ Hyp’ 21m 23 o …………….
Area and the Law of Sines. A B C a b c h The area, K, of a triangle is K = ½ bh where h is perpendicular to b (called the altitude). Using Right Triangle.
Area of a Triangle A B 12cm C 10cm Example 1 : Find the area of the triangle ABC. 50 o (i)Draw in a line from B to AC (ii)Calculate height BD D (iii)Area.
This triangle will provide exact values for
Trigonometry Sine Rule Finding a length Sine Rule Finding an Angle
Draw a 9cm line and label the ends A and B. This is the line AB.
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.
Introduction This Chapter involves the use of 3 formulae you saw at GCSE level We will be using these to calculate missing values in triangles We will.
EXAMPLE 1 Solve a triangle for the AAS or ASA case Solve ABC with C = 107°, B = 25°, and b = 15. SOLUTION First find the angle: A = 180° – 107° – 25° =
We are now going to extend trigonometry beyond right angled triangles and use it to solve problems involving any triangle. 1.Sine Rule 2.Cosine Rule 3.Area.
Note 8– Sine Rule The “Ambiguous Case”
Created by Mr. Lafferty Maths Dept.
The Sine Rule The Sine Rule is used for cases in which the Cosine Rule cannot be applied. It is used to find: 1. An unknown side, when we are given two.
S4 Credit Exact values for Sin Cos and Tan Angles greater than 90o
Drawing a sketch is always worth the time and effort involved
Whiteboardmaths.com © 2004 All rights reserved
The Sine Rule The Cosine Rule
hypotenuse opposite adjacent Remember
Warm-Up Exercises ABC Find the unknown parts of A = 75°, B 82°, c 16
Use of Sine, Cosine and Tangent
The Sine Rule The Sine Rule is used for cases in which the Cosine Rule cannot be applied. It is used to find: 1. An unknown side, when we are given two.
6-3: Law of Cosines
The Area of a Triangle A C B
Triangle Starters Pythagoras A | Answers Pythagoras B | B Answers
Bell Work Find the measure of angle A Find x. A 7” 9” 30° 10” x.
The General Triangle C B A.
Starter Sketch a regular pentagon
We are Learning to…… Use The Cosine Law.
We are Learning to…… Use The Sine Law.
Starter Construct accurately two different triangles with sides 3 cm and 5 cm and an angle of 30° opposite the 3 cm side Use a ruler, protractor and compasses.
The Sine Rule The Sine Rule is used for cases in which the Cosine Rule cannot be applied. It is used to find: 1. An unknown side, when we are given two.
Law of Sines and Cosines
The General Triangle C B A.
The General Triangle Tuesday, 09 April 2019.
Triangles that aren’t Right Angled
The Sine Rule The Sine Rule is used for cases in which the Cosine Rule cannot be applied. It is used to find: 1. An unknown side, when we are given two.
Trigonometry To be able to find missing angles and sides in right angled triangles Starter - naming sides.
Pythagoras Theorem Example
Unit 9. Day 17..
Warm Up – 2/27 - Thursday Find the area of each triangle.
Trigonometry rules Sunday, 28 July 2019.
The Sine Rule. A B C ao bo co.
The Cosine Rule. A B C a b c a2 = b2 + c2 -2bccosAo.
The Cosine Rule. A B C a b c a2 = b2 + c2 -2bccosAo.
THE SINE RULE Powerpoint hosted on
Presentation transcript:

Example 1 : Find the area of the triangle ABC. Area of a Triangle Example 1 : Find the area of the triangle ABC. B (i) Draw in a line from B to AC (ii) Calculate height BD 10cm 7.66cm 50o D (iii) Area A C 12cm

Example 2 : Find the area of the triangle PQR. Area of a Triangle Example 2 : Find the area of the triangle PQR. P (i) Draw in a line from P to QR (ii) Calculate height PS 12cm 7.71cm 40o S (iii) Area Q R 20cm

Area of ANY Triangle Learning Intention Success Criteria 1. To explain how to use the Area formula for ANY triangle. Know the formula for the area of any triangle. 2. Use formula to find area of any triangle given two length and angle in between.

General Formula for Area of ANY Triangle Bo Co a b c h Consider the triangle below: Area = ½ x base x height What does the sine of Ao equal Change the subject to h. h = b sinAo Substitute into the area formula

Area of ANY Triangle B B a c C C b A A Key feature To find the area you need to knowing 2 sides and the angle in between (SAS) Area of ANY Triangle The area of ANY triangle can be found by the following formula. B B a Another version c C C Another version b A A

Example : Find the area of the triangle. Area of ANY Triangle Example : Find the area of the triangle. B B The version we use is 20cm c C C 30o 25cm A A

Example : Find the area of the triangle. Area of ANY Triangle Example : Find the area of the triangle. E The version we use is 10cm 60o 8cm F D

What Goes In The Box ? Key feature Remember (SAS) Calculate the areas of the triangles below: (1) 23o 15cm 12.6cm A =36.9cm2 (2) 71o 5.7m 6.2m A =16.7m2

Sine Rule Learning Intention Success Criteria 1. To show how to use the sine rule to solve REAL LIFE problems involving finding the length of a side of a triangle . Know how to use the sine rule to solve REAL LIFE problems involving lengths.

Sine Rule B a c C b A The Sine Rule can be used with ANY triangle Works for any Triangle The Sine Rule can be used with ANY triangle as long as we have been given enough information. B a c C b A

The Sine Rule Deriving the rule C b a B A c This can be extended to Consider a general triangle ABC. Deriving the rule P Draw CP perpendicular to BA This can be extended to or equivalently

Calculating Sides Using The Sine Rule Example 1 : Find the length of a in this triangle. B 10m 34o 41o a C A Match up corresponding sides and angles: Rearrange and solve for a.

Calculating Sides Using The Sine Rule Example 2 : Find the length of d in this triangle. D 10m 133o 37o d E C Match up corresponding sides and angles: Rearrange and solve for d. = 12.14m

What goes in the Box ? Find the unknown side in each of the triangles below: (1) 12cm 72o 32o a (2) 93o b 47o 16mm a = 6.7cm b = 21.8mm

Sine Rule Learning Intention Success Criteria 1. To show how to use the sine rule to solve problems involving finding an angle of a triangle . Know how to use the sine rule to solve problems involving angles.

Calculating Angles Using The Sine Rule B Example 1 : Find the angle Ao A 45m 23o 38m C Match up corresponding sides and angles: Rearrange and solve for sin Ao = 0.463 Use sin-1 0.463 to find Ao

Calculating Angles Using The Sine Rule 143o 75m 38m X Example 2 : Find the angle Xo Z Y Match up corresponding sides and angles: Rearrange and solve for sin Xo = 0.305 Use sin-1 0.305 to find Xo

What Goes In The Box ? Bo Ao Calculate the unknown angle in the following: (2) 14.7cm Bo 14o 12.9cm (1) 14.5m 8.9m Ao 100o Ao = 37.2o Bo = 16o