International Young Naturalist’s Tournament

Slides:



Advertisements
Similar presentations
Notes # ____ 12.4 Tangent Ratio.
Advertisements

Trigonometry Right Angled Triangle. Hypotenuse [H]
Sine, Cosine, Tangent, The Height Problem. In Trigonometry, we have some basic trigonometric functions that we will use throughout the course and explore.
Right Triangle Trigonometry Day 1. Pythagorean Theorem Recall that a right triangle has a 90° angle as one of its angles. The side that is opposite the.
Slide Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
9.6 Solving Right Triangles Inverse of the trigonometric functions.
Right Triangle Trigonometry Find the value of trigonometric functions of acute angles Use the complementary angle theorem Solve right triangles Solve applied.
1 Right Triangle Trigonometry.. opposite hypotenuse adjacent hypotenuse adjacent opposite reference angle Anatomy of a Right Triangle.
Trigonometry Day 2 Need Class Sets (1/2 set for sleeves) for today: Applications for Trig. – Angles of Elev. & Depr.
 In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs  a 2 + b 2 = c 2 a, leg.
Geometry Notes Lesson 5.3A – Trigonometry T.2.G.6 Use trigonometric ratios (sine, cosine, tangent) to determine lengths of sides and measures of angles.
Geometry Notes Lesson 5.3B Trigonometry
 A trigonometric ratio is a ratio of the lengths of 2 sides of a right triangle.  You will learn to use trigonometric ratios of a right triangle to determine.
Honors Geometry Sections 10.1 & 10.2 Trigonometric ratios
The Basics State the RatioSidesAnglesReal-Life
STARTER x x In each triangle, find the length of the side marked x.
Right Triangle Trigonometry
Trigonometric Functions
7.2 Right Triangle Trigonometry. A triangle in which one angle is a right angle is called a right triangle. The side opposite the right angle is called.
4.3 Right Triangle Trigonometry
A grain auger lifts grain from the ground to the top of a silo. The greatest angle of elevation that is possible for the auger is 35 o. The auger is 18m.
4.3 Right Triangle Trigonometry
Set calculators to Degree mode.
7.2 Finding a Missing Side of a Triangle using Trigonometry
TRIGONOMETRY BASIC TRIANGLE STUDY: RATIOS: -SINE -COSINE -TANGENT -ANGLES / SIDES SINE LAW: AREA OF A TRIANGLE: - GENERAL -TRIGONOMETRY -HERO’S.
6.1 Law of Sines. Introduction Objective: Solve oblique triangles To solve: you must know the length of one side and the measures of any two other parts.
Warm-Up: For the right triangle ABC shown below, find the values of b and c. Hint: Hint: Think about the side you know, the side you want to find out,
9.5 Trigonometric Ratios Advanced Geometry.
UNIT 5: TRIGONOMETRY Final Exam Review. TOPICS TO INCLUDE  Pythagorean Theorem  Trigonometry  Find a Missing Side Length  Find a Missing Angle Measure.
It’s for Trigonometric Functions and Right Triangles. 4.3 Right Triangle Trigonometry adjacent side opposite side hypotenuse.
© 2010 Pearson Prentice Hall. All rights reserved. CHAPTER 10 Geometry.
Geometry Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.
Trigonometry Chapters Theorem.
13.1 Right Triangle Trigonometry. Trigonometry: The study of the properties of triangles and trigonometric functions and their applications. Trigonometric.
Lesson 46 Finding trigonometric functions and their reciprocals.
Chapter 4 Section 3 Right triangle trigonometry. Objectives Evaluate trigonometric functions of acute angles Use fundamental trigonometric identities.
9.5: Trigonometric Ratios. Vocabulary Trigonometric Ratio: the ratio of the lengths of two sides of a right triangle Angle of elevation: the angle that.
Trigonometric Ratios Section 8.1. Warm Up State the following: 1.Angle opposite AB 2.Side opposite angle A 3.Side opposite angle B 4.Angle opposite AC.
[8-3] Trigonometry Mr. Joshua Doudt Geometry pg
4.3 Right Triangle Trigonometry Right Triangle Trig Our second look at the trigonometric functions is from a ___________________ ___________________.
Algebra 2 cc Section 7.1 Solve right triangles “Trigonometry” means triangle measurement and is used to solve problems involving triangle. The sides of.
6.2 Trig of Right Triangles Part 1. Hypotenuse Opposite Adjacent.
Right Triangle Trigonometry A B C SOHCAHTOA. Geometry - earth measurement Trigonometry - triangle measurement Sine of an angle = Opposite leg Hypotenuse.
5.2 Trigonometric Ratios in Right Triangles. A triangle in which one angle is a right angle is called a right triangle. The side opposite the right angle.
Section 9.5: Trigonometric Ratios. trigonometric ratio – a ratio of the lengths of two sides of a right triangle. The three basic trigonometric ratios.
Right Triangle Trigonometry
10.3 Solving Right Triangles
Grade 10 Academic (MPM2D) Unit 5: Trigonometry Slope and Angle (Elevations & Depressions) Mr. Choi © 2017 E. Choi – MPM2D - All Rights Reserved.
-- How to solve right triangles
Trigonometric Functions
Right Triangles Trigonometry
Solving Practical Problems Using Trigonometry
7-6 Sine and Cosine of Trigonometry
Angles of Elevation and Depression
Trig Functions – Learning Outcomes
Mountain Peaks.
You will need a calculator and high lighter!
CHAPTER 8 Right Triangles.
CHAPTER 10 Geometry.
7-4: Trigonometry.
Aim: How do we review concepts of trigonometry?
Objectives Understand and use trigonometric relationships of acute angles in triangles. Determine side lengths of right triangles by using trigonometric.
Angles of Elevation and Depression
Right Triangle Trigonometry
Introduction to Trigonometry
Trigonometry for Angle
Trigonometry Ratios in Right Triangles
Trigonometric Ratios Geometry.
Reviewing Trig Ratios 7.4 Chapter 7 Measurement 7.4.1
Right Triangle Trigonometry
Presentation transcript:

International Young Naturalist’s Tournament IYNT 2016 Iran-Shiraz International Young Naturalist’s Tournament

#problem number 15 mountain speak Reporter : Mahdiyeh Shahrabi Maple group

15. Mountain Peaks What methods are used to determine the elevation of the World’s highest mountains? Suggest your own experimental method and determine the height of a mountain or a hill of your choice.

Al-Biruni'sClassic Experiment. Method professional Altimetry SAR Altimetry Theodolite experimental Temperature of air Al-Biruni'sClassic Experiment. Using a Clinometer Shadow of the mountain

Satellite altimetry Function

SAR Altimetry (synthetic aperture radar)

Theodolite

Temperature of air For example if the air temperature at top of mountain is -10 degrees and 20 degrees in the hillside , altitude mountain will be 5000 meters

Al-Biruni'sClassic Experiment Angle of elevation Al-Biruni'sClassic Experiment Using a Clinometer

Knowledge of trigonometry Angle of elevation An astrolabe Knowledge of trigonometry

An astrolabe Clinometer

Al-Biruni's Classic Experiment •Angle of elevation of the mountain top at two different points lying on a straight line were measured using an astrolabe. The third being the distance between these two points. Al-Biruni's Classic Experiment

H= E+D Tan(a) Elevation of mountain= height of Clinometer + distance to mountain tan of angle H= E+D Tan(a)

Use knowledge of trigonometry sine

sine the trigonometric function that is equal to the ratio of the side opposite a given angle (in a right triangle) to the hypotenuse