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.
| b2 + a2 |
= |
c2 |
| b2 + (23.5)2 |
= |
(42.7)2 |
| b2 + 552.25 |
= |
1823.29 |
| b2 |
= |
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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