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32 Part I: Technical Mathematics
Part I.D
( )= ( )=
sin A sin 49 0.
7547
opposite side
hypotenuse = 0.
7547
6
= 0.
7547
c
6
× c = 0.
7547 × c
c
6 = 0.
7547c
6 ÷ 0. 7547 = 0. 7547c
÷ 0.
7547
7.
950 = c
Now that we know the length of c, we can find the length of side b using the
Pythagorean theorem:
a + b = c
2 2 2
+ =( )
6 b 7.
950
2 2 2
6 + b 6 = ( 7.
950) 6
2 2 2 2 2
b
2
= 27.
2025
2
b = 27.
2025
b = 5.
216
Alternatively, we can use a trigonometric function to find the length of side b:
( )= ( )=
cot A cot 49 0.
8693
adjacent side
opposite side = 0.
8693
b
= 0.
8693
a
b
× 6 = 0.
8693×
6
6
b = 5216 .
INVERSE TRIGONOMETRIC FUNCTIONS
In some cases, we know the value of a trigonometric function for a particular
angle but do not know the degree measure of the angle. We can use an inverse trigonometric
function to solve for the angle. These inverse functions are of the form
sin –1 (x), cos –1 (x), tan –1 (x), cot –1 (x), sec –1 (x), csc –1 (x)