Unit 4  Objective 4  The Right Triangle
Given the right triangle:
The right angle is labeled C and the other two vertices
A and B. The side opposite A is side a, side opposite B
is side b, and side opposite C is side c, the hypotenuse.
Angles A and B are complementary since C is a right angle.
(A + B = 90°)
Examples:
1. 
Given A
= 55° and b = 7.92, solve the right triangle ABC.
Since A
= 55° then B
= 90°  55° = 35°
You could solve for side a by using tan
A = a/b.
tan 55 degrees 
= 
a / 7.92 
7.92 tan 55 degrees 
= 
a 
7.92 (1.428148) 
= 
a 
11.31 

a 
There is more than one way to solve for
side c. One possibility is:
sec A 
= 
c/b 
b sec A 
= 
c 
7.92 sec 55 degrees 
= 
c 
7.92 (1.7434468) 
= 
c 
13.81 

c 



2. 
Given a = 23.5
and c = 42.7, solve the right triangle ABC.
You could use the pythagorean theorem to solve for side
b.
b^{2} + a^{2} 
= 
c^{2} 
b^{2} + (23.5)^{2} 
= 
(42.7)^{2} 
b^{2} + 552.25 
= 
1823.29 
b^{2} 
= 
1271.04 
b 

35.75 
You could solve angle A by using:
sin A 
= 
23.5 / 42.7 
sin A 

0.5503513 
A 

33.4° 
B 
= 
90°  33.4° = 56.5° 


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