8.1 - Acute angles using RIGHT TRIANGLES
A triangle where one angle is
angle


90  rad  is a RIGHT TRIANGLE. In the figure below, the
2

is an ACUTE angle because
c
b

a
The RATIO of the sides of a right triangle can be defined as trigonometric function the angle 
Well known acronym to help recall the above definitions:
S O H C A H T O A
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Examples:
In the right triangle below, let B  30
c
and b = 8 cm, find side c exactly.
b
B
a
In the right triangle below, let B  30
c
and a = 5 in., find side b exactly.
b
B
a
In the right triangle below, let A  60
and b = 8, find side c exactly.
A
c
b
a
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Complementary Angles
Two ACUTE angles are COMPLEMENTARY if their sum is 90
A
c
b
B
a
** CoFunctions of complimentary angles are Equal **
In the right triangle below, let a = 6 and A  40 , find b, c, and angle B, approximate to two
decimal places.
A
c
B
b
a
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Applications
A flagpole in my front yard standing 55 feet tall has an angle of elevation of 400 with my front
porch steps. What is the distance from the porch to the flagpole?
A wire is connected to a hook 24 feet away from the base of my house to a gutter 38 feet up.
What is the angle of declination the wire makes with the gutter?
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