Finding Unknown Angles

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Grade 9: The Learning Equation Math

31.03: Finding Unknown Angles

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Measurement

Refresher pp 62-63

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Prerequisite Skills:

explain, in more than one way, why the sum of the measures of the angles of a triangle is 180�.

Solve equations with one variable.

Review skills from first 2 lessons:

Explain the meaning of sine, cosine, and tangent ratios in right triangles.

Ratios in Right Triangles: Grade 9 Lesson 31.01

Use sine, cosine, and tangent ratios to calculate side lengths and angle measures in a right triangle.

Ratios in Right Triangles: Grade 9 Lesson 31.02
Finding Unknown Angles: Grade 9 Lesson 31.03

use the or keys on a scientific calculator.

Ratios in Right Triangles: Grade 9 Lesson 31.01
Finding Unknown angles: Grade 9 Lesson 31.02

Apply the Pythagorean relationship.

Ratios in Right Triangles: Grade 9 Lesson 31.02

acute, angle, trigonometry, right triangle, sine, cosine, tangent, hypotenuse, opposite side, adjacent side

Note: acute and angle need to be added to this puzzle.

Learning Outcomes:

The student will:

use the fact that angles in a triangle sum to 180 degrees to calculate angle measures.

Sum of Three Angles in a Triangle is 180^o

If you know the sum of the angles of any triangle is 180^o, you do not need trigonometry functions to calculate the size of an angle when the other two angles are known. The following applet will help you visualize an important triangle calculation tool:

<A + <B + <C = 180^o

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Sum of Angles in a Triangle

The following animation shows why the sum of the angles in any triangle is 180�. Remember to click [Go] to move to next animation.

use sine, cosine, and tangent ratios to calculate angles in a right triangle with and without scientific calculators.

Review "Soh Cah Toa" and Reference Angles

Practice

The "Introduction" reviews the Pythagorean theorem. "Naming Sides" reviews the trigonometry triangle names required to use "Soh Cah Toa". The "Practice" section has 5 sections of problem types. For this activity complete problem types 10 - 12. The activity below this one focuses on the same 3 problem types.

Problem Types 1-3: Pythagorean Theorem.
Problem Types 4-6: Calculate the sine, cosine and tangent ratios given one reference angle.
Problem Types 7-9: Calculate the sine, cosine and tangent ratios given two appropriate sides.
Problem Types 10-12: Calculate the reference angle given two appropriate sides.
Problem Types 13-18: Calculate the length of one of the sides given appropriate side and reference angle.

Using Trigonometry to Calculate Angles

If we know the length of two sides of a right triangle ABC we can calculate the size of either acute angle using one of the trigonometry functions. The buttons below show the sides and trigonometry function you will need to calculate an angle. Click each "A" button to learn how to calculate the angle using our 3 trigonometry functions.

<A =

(100th)

You need a Java2 enabled browser or install the Java2 plug-in

Original source: Pythagoras and Trigonometry

Click Reload/Refresh if the calculator does not display properly.

Review:

pythagorean_triangle.jpg (3622 bytes) Triangles also have sides. If you know the length of two sides of a right triangle, you do not need to use trigonometry functions.

You can calculate the length of the third using the Pythagorean Theorem.

a² + b² = c²

Pythagoras Theorem - interactive proof

History of Pythagoras

In the second part of the last lesson helped you learn how to calculate side lengths using the various trigonometry functions when one side and one acute angle are known. Click a button to see examples of how to calculate that side using a trigonometry function.
Sine ratio S = o/h	Cosine ratio C = a/h	Tangent ratio T = o/a
/	/	/

sinD = 4/5	<D =	= 53.1^o(tenth)
cosD = 3/5	<D =	= 53.1^o(tenth)
tanD = 4/3	<D =	= 53.1^o(tenth)
sinE = 3/5	<E =	= 36.9^o(tenth)

Trigonometry Calculator

The following site will show you how to use the trigonometry ratios to calculate the lengths of a side in in a right triangle.

Right Angle Relationships

To use:

Fill in a value for 1 of the 3 sides,
fill in a value for angle D or E.
put a question mark, (?), in the box of the side whose length you are trying to find,
then click "Go" to see how to find the measure of your angle.

An example has been completed for you. Remove these and substitute your own values to investigate right angle triangles further.

Quia! Challenge Board - Introductory Trigonometry

Enrichment:

Sum of Angles in a Triangle

Polygon Angle Applet

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Comments to: Jim Reed

Hit Counter visitors since September 3, 2000

Sum of Three Angles in a Triangle is 180o