Solving Right Triangles

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Solving Right Triangles

• Anthony D Coley, Ed. S.
• Edited by Judy Stoops, EdM

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Objectives

• To determine the measures of all six parts of a
  right triangle (3 angles 3 sides) given
• Two side lengths
• One side length and one acute angle measure

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Recall Every right triangle has . . .

• One (1) right angle
• Two (2) acute angles
• One (1) hypotenuse
• Two (2) legs

Definition To SOLVE A RIGHT TRIANGLE means to
determine the measures of all six parts.
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To solve a right triangle you must know either of
the following
1. One side length and one acute angle measure
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2. Two side lengths
C is easily calculated to be 5. One angle is 90.
How do we find the others?
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Once you know the sine, the cosine or the tangent
of an acute angle, you can use a calculator to
find the measure of the angle.
In general, for an acute angle ?, if sin ? x,
then sin-1 x ? if cos ? y, then cos-1y
? if tan ? z, then tan-1z ?
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Let's look at the problem of finding angles if
you know the sides. Again, we will use the
trigonometric ratios, but in reverse.
c 5
a 3
A
b 4
sinA 0.6, cosA 0.8 and tanA 0.75
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Using the inverse trigonometric ratios, we
have sinA 0.6, then A sin-10.6
36.9o cosA 0.8, then A cos-10.8
36.9o tanA 0.75, then A tan-10.75 36.9o
NOTE Make sure your calculator is in degree
mode ?
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Example Solve the right triangle.
tanB 2/3 0.667 B tan-1 0.667 B 33.7o
mltA 90 mltB 90 33.7
56.3o
The side lengths of the triangle are 2, 3, and
about 3.6. The triangle has one right angle and
two acute angles whose measures are about 33.7o
and 56.7o.
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Example Solve the right triangle.
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k
Example Solve the right triangle.
J
H
25o
h
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K
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Example Solve the right triangle.
y
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Assignment

• Pg 570 22-30 even,33
• Worksheet Applications of Trigonometry
• Chapter 9 Review
• Chapter 9 Test on Wednesday, April 18