Problems using Trigonometry
and Pythagoras' Theorem
In the first part of the second lesson you learned to
calculate the third side when the other two sides of a right triangle are known using the Pythagorean
Theorem:
a2 + b2 = c2
The second part of lesson two helped you learn how to calculate side
lengths using the various trigonometry functions when one side and one acute angle are
known.
In the first part of the last lesson you
reviewed the sum of angles in a triangle. Remember:
<A + <B + <C = 180o
The second part of the last lesson taught how we can calculate the size of
either acute angle using one of the trigonometry functions when two of the sides of
triangle ABC are known.
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.
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.
Problems using
Trigonometry and Pythagoras' Theorem
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.
