CK-12-Pre-Calculus Concepts

http://www.ck12.org Chapter 4. Basic Triangle Trigonometry

• 3, 4, 5


• 5, 12, 13


• 7, 24, 25


• 8, 15, 17


• 9, 40, 41

More Pythagorean number triples can be found by scaling any other Pythagorean number triple. For example:
3 , 4 , 5 → 6 , 8 ,10 (scaled by a factor of 2)
Even more Pythagorean number triples can be found by taking any odd integer like 11, squaring it to get 121, halving
the result to get 60.5. The original number 11 and the two numbers that are 0.5 above and below (60 and 61) will
always be a Pythagorean number triple.
112 + 602 = 612
Example A
A right triangle has two sides that are 3 inches. What is the length of the third side?
Solution:Since it is a right triangle and it has two sides of equal length then it must be a 45-45-90 right triangle. The
third side is 3

√

2 inches.
Example B
A 30-60-90 right triangle has hypotenuse of length 10. What are the lengths of the other two sides?
Solution:The hypotenuse is the side opposite 90. Sometimes it is helpful to draw a picture or make a table.

TABLE4.2:

30 60 90

x x√ 3 2 x

10

From the table you can write very small subsequent equations to solve for the missing sides.

10 = 2 x

x= 5

x

√

3 = 5

√

3

Example C
A 30-60-90 right triangle has a side length of 18 inches corresponding to 60 degrees. What are the lengths of the
other two sides?
Solution:Make a table with the side ratios and the information given, then write equations and solve for the missing
side lengths.

TABLE4.3:

30 60 90