Carpentry & Building Construction © 2004

Math Activities :

Self-Check Math Activity 29

Finding Angles and Measurements Using Cosine

With a right triangle, you can find the size of angles or sides using trigonometric functions and tables. One function is cosine. The cosine of an acute angle equals the adjacent side divided by the hypotenuse.

The formula is cos x =	adjacent side

	hypotenuse

The cosine of an angle can be found by using the Table of Trigonometric Values. Or, you can use the cosine function on a scientific calculator.

Terms, Symbols, & Abbreviations
right triangle-a triangle with one right (90-degree) angle
cosine-a math function that is the ratio between the side next to an acute angle and the hypotenuse
acute angle -an angle less than 90 degrees
hypotenuse -the side of a right triangle that is opposite the right angle

Practice Exercise

Find side b when the hypotenuse is 16'' and the acute angle is 23º.

Step 1

cos x =	adjacent side

	hypotenuse

Step 2

23 degrees = .9205 (from Table of Trigonometric Values)

Step 3

.9205 =	adjacent side

	16

Step 4

.9205 × 16 = adjacent side, or side b

Step 5

14.728'' = side b

Problem Exercises
Table of Trignometric Values (10.0K)

Find the missing side for each right triangle.


1.	Find the adjacent side of the triangle when the angle is 30º and the hypotenuse is 16''.
		A)	26.856''
		B)	26.500''
		C)	13.856''
		D)	13.500''


2.	Find the adjacent side of the triangle when the angle is 35º and the hypotenuse is 40''.
		A)	32.768''
		B)	32.819''
		C)	32.574''
		D)	32.700''


3.	Find the adjacent side of the triangle when the angle is 38º and the hypotenuse is 27''.
		A)	27.788''
		B)	27.276''
		C)	21.788''
		D)	21.276''


4.	Find the adjacent side of an exterior trim piece when the angle is 32º and the hypotenuse is 50''.
		A)	51.529''
		B)	42.400''
		C)	31.245''
		D)	26.495''


5.	Find the adjacent side of a corner brace when the angle is 45º and the hypotenuse is 8''.
		A)	4.6947''
		B)	4.7071''
		C)	5.6568''
		D)	6.7193''