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W. 10: Principles of Trigonometry
JOSUE .VAZQUEZ RODRIGUEZ
Created on March 22, 2025
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Transcript
W. 10: Principles of Trigonometry
ACADEMY OF MATHEMATICS
INITIAL PROBLEM
A group of biology students is conducting a study on the height of sequoia trees in a national park. To do this, they use a theodolite to measure the angle of elevation from two different points. From point A, located 150 meters from the base of a tree, the angle of elevation to the top of the tree is 52 degrees. From point B, located on the same straight line as point A and farther from the tree, the angle of elevation is 38 degrees. 1. Calculate the height of the sequoia tree. 2. Determine the distance between points A and B. 3. If a drone flies directly from point A to the top of the tree, what is the distance the drone travels?
01
Pythagoras' Theorem
A) PYTHAGORAS' THEOREM
A right angled triangle is a triangle which has a right angle in one corner. The side opposite the right angle is called the hypotenuse, and is the longest side of the triangle. The other two sides are called the legs of the triangle.
Pythagoras' Theorem is:
Activity
Applications of the Pythagorean Theorem (in Geometry)
Example 1
Applications of the Pythagorean Theorem (in Geometry)
Teacher's Lesson
Applications of the Pythagorean Theorem (in Geometry)
Example 2
Applications of the Pythagorean Theorem (in Geometry)
Teacher's Lesson
Applications of the Pythagorean Theorem (in Geometry)
Example 3
Applications of the Pythagorean Theorem (in Geometry)
Teacher's Lesson
Applications of the Pythagorean Theorem (in contextualized problems)
Converse of the Pythagoras' Theorem
Converse of the Pythagoras' Theorem
02
Trigonometric Ratios
First Definitions
Activity
Finding Side Lengths
If we are given the angles of a right angled triangle and the length of one side, we can use trigonometric ratios to find the other side length. You only need to identify the given sides (hyp, opp, adj)/angle and the corresponding trigonometric ratio.