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Grade 9:  The Learning Equation Math

31.05: Solving Right Triangle Problems

3icon.gif (4368 bytes)


Refresher pp 66-7

SeekAWord2ech.class Author

Prerequisite Skills:


Key Terms                 

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

Note: acute needs to be added to this puzzle.


Learning Outcomes:

The student will:


Problems using Trigonometry and Pythagoras' Theorem

The sum of the angles of any triangle is 180o.  If you know 2 of the three angles of a right triangle subtract the sum of the two angles from 180o to calculate the third angle.


trigtri.gif (2447 bytes)There are 18 basic types of questions you can solve with the Pythagorean Theorem and trigonometry.  The first 3 types in the "Questions" section are devoted to Pythagoras's Theorem.     If you know 2 of the three sides of a right triangle use the Pythagorean Theorem to calculate the third side.

The last 15 types involve trigonometry functions.  These types are also organized into groups of three similar functions.  After completing two of these you will probably know what to do in the third one before looking at the examples.

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.

  • 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 using trigonometry functions.
  • Problem Types 13-18: Calculate the length of one of the sides given appropriate side and reference angle using trigonometry functions.



Study these examples:

Example 1

wpeED.jpg (3380 bytes)

Since wpeEE.jpg (821 bytes)ABC in the diagram above is a right triangle, we can use the Pythagorean Theorem:

a2 + b2 = c2

122 + b2 = 202

b2 = 202 - 122

b2 = 400 - 144 = 256

b = 256 wpeEF.jpg (789 bytes) =16 cm

We can use any two sides and the appropriate trigonometry ratio to find one of the missing sides.

tan A = opp/adj = a/b = 12/16 = 0.75

<A = tan-1(0.75)

<A = 0.75 wpe7.jpg (761 bytes) wpe7.jpg (761 bytes) = wpeF0.jpg (1591 bytes)

<A = 36.9o (nearest tenth)

The sum of the angles in a triangle is 180o.

A + B + C = 180

36.9 + B + 90 = 180

B = 53.1o

Example 2

ABCD is the end wall in an attic.  Segment AB is the sloping ceiling.

AD = 1600 mm; <A = 56 degrees

Ramona decides to hide a large gift box, DEGF, in the attic. If the box is 600 mm high, what is its length?



Answer questions #4 -12 on page 65 of the  Student Refresher.


Ferris Wheel Tracing Sinusoidal Curve

Can you see the sinusoidal curve traced out by the ferris wheel. Click on the ferris wheel to study the pattern in more detail..




Problem Solving Steps

Problems using Trigonometry and Pythagoras' Theorem

trigtri.gif (2447 bytes)The following is an earlier version of the flash object included in the previous section.  It will be useful to see questions generated where the triangle is not to scale.




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

Original source:  Pythagoras and Trigonometry



Reload/Refresh if the calculator does not display properly.



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.



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Comments to:  Jim Reed
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