Transcript 7.6 corrected

7.6 Law of Sines
• Use the Law of Sines to solve triangles and
problems
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In trigonometry, we can use the
Law of Sines to find missing parts of
triangles that are not right triangles.
A
Law of Sines:
In ABC,
c
b
sin A = sin B = sin C
a
b
c
C
a
B
Find p. Round to the nearest tenth.
Law of Sines
Cross products
Divide each side by sin
Use a calculator.
Answer:
to the nearest degree in
,
Law of Sines
Cross products
Divide each side by 7.
Solve for L.
Use a calculator.
Answer:
a. Find c.
Answer:
b. Find mT to the nearest degree in RST if r = 12,
t = 7, and mR = 76.
Answer:
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The Law of Sines can be used to “solve a
triangle,” which means to find the
measures of all of the angles and all of
the sides of a triangle.
. Round
angle measures to the nearest degree and side
measures to the nearest tenth.
We know the measures of two angles of the triangle. Use
the Angle Sum Theorem to find
Angle Sum Theorem
Add.
Subtract 120 from each side.
Since we know
and f, use proportions involving
To find d:
Law of Sines
Substitute.
Cross products
Divide each side by sin 8°.
Use a calculator.
To find e:
Law of Sines
Substitute.
Cross products
Divide each side by sin 8°.
Use a calculator.
Answer:
Round angle
measures to the nearest degree and side measures
to the nearest tenth.
We know the measure of two sides and an angle opposite
one of the sides.
Law of Sines
Cross products
Divide each side by 16.
Solve for L.
Use a calculator.
Angle Sum Theorem
Substitute.
Add.
Subtract 116 from each side.
Law of Sines
Cross products
Divide each side by sin
Use a calculator.
Answer:
a. Solve
Round
angle measures to the nearest degree and side
measures to the nearest tenth.
Answer:
b.
Round angle
measures to the nearest degree and side measures to
the nearest tenth.
Answer:
A 46-foot telephone pole tilted at an angle of from
the vertical casts a shadow on the ground. Find the
length of the shadow to the nearest foot when the
angle of elevation to the sun is
Draw a diagram Draw
Then find the
Since you know the measures of two angles of the
triangle,
and the length of a side
opposite one of the angles
you
can use the Law of Sines to find the length of the shadow.
Law of Sines
Cross products
Divide each side by sin
Use a calculator.
Answer: The length of the shadow is about
75.9 feet.
A 5-foot fishing pole is anchored to the edge of a
dock. If the distance from the foot of the pole to the
point where the fishing line meets the water is 45 feet,
about how much fishing line that is cast out is above
the surface of the water?
Answer: About 42 feet of the fishing line that is cast out
is above the surface of the water.
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Pre-AP Geometry:
Pg. 381 #15, 16 – 32 evens, 42
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Geometry:
Pg. 381 #15, 16 – 28 evens