Unit 4 - Objective 4 - The Right Triangle


Given the right triangle:

u4obj4-1.gif (1868 bytes)

The right angle is labeled C and the other two vertices A and B.  The side opposite anglew.gif (299 bytes)A is side a, side opposite anglew.gif (299 bytes)B is side b, and side opposite anglew.gif (299 bytes)C is side c, the hypotenuse.   Angles A and B are complementary since anglew.gif (299 bytes)C is a right angle. (anglew.gif (299 bytes)A + anglew.gif (299 bytes)B = 90)

Examples:

1.

Given angle.gif (312 bytes)A = 55 and b = 7.92, solve the right triangle ABC.

Since angle.gif (312 bytes)A = 55 then angle.gif (312 bytes)B = 90 - 55 = 35

u4obj4-2.gif (1914 bytes)

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 approx_g.gif (145 bytes) 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 approx_g.gif (145 bytes) c

2.

Given a = 23.5 and c = 42.7, solve the right triangle ABC.

u4obj4-3.gif (2777 bytes)

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 approx_g.gif (145 bytes) 35.75

You could solve angle A by using:

sin A = 23.5 / 42.7
sin A appro2_g.gif (178 bytes) 0.5503513
angle.gif (312 bytes)A approx_g.gif (145 bytes) 33.4
angle.gif (312 bytes)B = 90 - 33.4 = 56.5

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