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

Note: acute needs to be added to this puzzle.

Problems using Trigonometry and Pythagoras' Theorem

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

Example 1

Since 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 =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 =

<A = 36.9^o (nearest tenth)

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

A + B + C = 180

36.9 + B + 90 = 180

B = 53.1^o

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.

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.