Transcript Angles, Degrees, and Special Triangles

Solving Right Triangles
Trigonometry
MATH 103
S. Rook
Overview
• Section 2.3 in the textbook:
– Solving simple right triangles
– Solving more complex problems with right
triangles
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Solving Simple Right Triangles
Solving Simple Right Triangles
• We are now ready to solve for unknown components
in right triangles in general:
– ALWAYS draw a diagram and mark it up with the given
information as well as what is gained while working
the problem
– When given two sides, we can obtain the third side
using the Pythagorean Theorem
– When given two angles, we can obtain the third angle
by subtracting the sum from 180°
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Solving Simple Right Triangles
(Continued)
– When given one angle and one side, we can obtain
another side via a trigonometric function
• SOHCAHTOA
– When given two sides, we can obtain an angle via an
inverse trigonometric function
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Solving Simple Right Triangles
(Example)
Ex 1: Refer to right triangle ABC with C = 90°. In
each, solve for the remaining components:
a) A = 41°, a = 36 m
b) a = 62.3 cm, c = 73.6 cm
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Solving More Complex Problems
with Right Triangles
Solving More Complex Problems
with Right Triangles
• More complex problems will contain multiple
triangles and/or figures, but the process still
remains the same:
– ALWAYS draw and mark up a diagram!
– Calculations may require multiple steps
– Sometimes there is more than one way to arrive
at the desired answer
• Only way to become proficient is to
practice!!!
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Solving More Complex Problems
with Right Triangles (Example)
Ex 2: The circle has a radius of r and center at C.
The distance from A to B is x. If C = 65° and
x = 22, find: a) r b) y
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Solving More Complex Problems
with Right Triangles (Example)
Ex 3: The distance from D to C is x. If A = 32°,
angle BDC = 48°, and AB = 56, find: a) h b) x
c) angle ABD
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Solving More Complex Problems
with Right Triangles (Example)
Ex 4: Each edge of the cube is 5 inches long.
Find the measure of the angle formed by
diagonals CF and CH:
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Summary
• After studying these slides, you should be able
to:
– Solve problems containing right triangles
• Additional Practice
– See the list of suggested problems for 2.3
• Next lesson
– Applications (Section 2.4)
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