Law of Sines
and
Law of Cosines
Examples / Practice
Find p. Round to the nearest tenth.
to the nearest degree in
,
Law of Sines
Cross products
Divide each side by 7.
a. Find c.
Answer:
b. Find mT to the nearest degree in RST if r = 12,
t = 7, and mT = 76.
Answer:
. 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
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
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
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.
Use the Law of Cosines since the measures of two sides and the
included angle are known.
Law of Cosines
Simplify.
Take the square root of
each side.
Use a calculator.
Answer:
Answer:
Law of Cosines
Simplify.
Subtract 754 from each side.
Divide each side by –270.
Solve for L.
Use a calculator.
Answer:
Answer:
Determine whether the Law of Sines or the Law of Cosines
should be used first to solve
Then solve
Round
angle measures to the nearest degree and side measures to
the nearest tenth.
Since we know the measures of two sides and the included
angle, use the Law of Cosines.
Law of Cosines
Take the square root of
each side.
Use a calculator.
Next, we can find
If we decide to find
we
can use either the Law of Sines or the Law of Cosines to find this
value. In this case, we will use the Law of Sines.
Law of Sines
Cross products
Divide each side by 46.9.
Take the inverse of each
side.
Use a calculator.
Use the Angle Sum Theorem to find
Angle Sum Theorem
Subtract 168 from each
side.
Answer:
Determine whether the Law of Sines or the Law of Cosines
should be used first to solve
Then solve
Round
angle measures to the nearest degree and side measures to
the nearest tenth.
Answer:
AIRCRAFT From the diagram of the plane shown, determine
the approximate exterior perimeter of each wing. Round to
the nearest tenth meter.
Since
is an isosceles triangle,
Use the Law of Sines to find KJ.
Law of Sines
Cross products
Divide each side by sin
Simplify.
.
Use the Law of Sines to find
.
Law of Sines
Cross products
Divide each side by 9.
Solve for H.
Use a calculator.
Use the Angle Sum Theorem to find
Angle Sum Theorem
Subtract 95 from each side.
Use the Law of Sines to find HK.
Law of Sines
Cross products
Divide each side by sin
Use a calculator.
The perimeter of the wing is equal to
Answer: The perimeter is about
about 67.1 meters.
or
The rear side window of a station wagon has the shape shown
in the figure. Find the perimeter of the window if the length of
DB is 31 inches.
Answer: about 93.5 in.