Carpentry & Building Construction © 2004

Math Activities :

Self-Check Math Activity 28

Finding Angles and Measurements Using Sine

Carpenters must make sure that walls and floors are square as they work. Diagonal lines may be drawn on rectangular surfaces to check for squareness. The diagonals create two right triangles on a surface.

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

The formula is sine x =	opposite side

	hypotenuse.

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

Terms, Symbols, & Abbreviations
right triangle-a triangle with one right (90-degree) angle
sine-a math function that is the ratio between the side opposite 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
altitude-the vertical side of a triangle

Practice Exercise

Find the altitude(a) of a triangle when the hypotenuse is 16'' and the acute angle is 23º.

Step 1

sine x =	opposite side

	hypotenuse.

Step 2

sine 23 degrees = .3907 (from Table of Trigonometric Values)

Step 3

.3907 =	opposite side

	16

Step 4

.3907 × 16 = opposite side, or a

Step 5

6.2512'' = a

Problem Exercises
Table of Trignometric Values (10.0K)


1.	Find the altitude of a triangle when the angle is 35º and the hypotenuse is 32''.
		A)	9.5736''
		B)	18.3552''
		C)	27.8192''
		D)	36.7002''


2.	Find the altitude of a triangle when the angle is 28º and the hypotenuse is 40''.
		A)	18.78''
		B)	27.6157''
		C)	36.7880''
		D)	45.7813''


3.	Find the altitude of a triangle when the angle is 23º and the hypotenuse is 47''.
		A)	18.0000''
		B)	18.3907''
		C)	18.3629''
		D)	18.9205''


4.	Find the altitude of a triangle when the angle is 30º and the hypotenuse is 50''.
		A)	10.866''
		B)	15.5''
		C)	20.75''
		D)	25''


5.	Find the altitude of a triangle when the angle is 45º and the hypotenuse is 25''.
		A)	8.8388''
		B)	17.6775''
		C)	26.5162''
		D)	35.3551''