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°