1. In ΔRST, mR = 63, mS = 38, and r = 52. Find s to
the nearest tenth.
2. In ΔRST, mS = 122, s = 10.8, and r = 5.2. Find mR
to the nearest degree.
3. Solve ΔMNP, if mM = 50, mN = 32, and m = 15.
Round angle measures to the nearest degree and side
measures to the nearest tenth.
4. Solve ΔMNP, if n = 8.5, p = 10.8, and mP = 110.
Round angle measures to the nearest degree and side
measures to the nearest tenth.
• Use the Law of Cosines to solve triangles.
• Solve problems by using the Law of Cosines.
• Law of Cosines
Two Sides and the Included Angle
Find x if y = 11, z = 25, and mX = 45.
Use the Law of Cosines since the measures of two
sides and the included angle are known.
Two Sides and the Included Angle
Law of Cosines
Simplify.
Take the square root
of each side.
Use a calculator.
Answer: x ≈ 18.9
Find r if s = 15, t = 32, and mR = 40. Round to the
nearest tenth.
A. 25.1
B. 44.5
C. 22.7
D. 21.1
A.
B.
C.
D.
A
B
C
D
Three Sides
Find mL.
Law of Cosines
Simplify.
Three Sides
Subtract 754 from each side.
Divide each side by –270.
Solve for L.
Use a calculator.
Answer: mL ≈ 48.8
Find mF. Round to the nearest tenth.
A. 151.9
B. 107.8
C. 19.7
D. 28.1
1.
2.
3.
4.
A
B
C
D
Select a Strategy
Determine whether the Law of Sines or the Law of
Cosines should be used first to solve ΔDEF. Then
solve ΔDEF. 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.
Select a Strategy
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.
Select a Strategy
Law of Sines
Cross products
Divide each side by 46.9.
Take the inverse of each
side.
Use a calculator.
Select a Strategy
Use the Angle Sum Theorem to find
Angle Sum Theorem
≈
Subtract 168 from each
side.
Answer: f ≈ 46.9, mD ≈ 23, mE ≈ 12
A. Determine whether the Law of Sines or the Law of
Cosines should be used first to solve ΔABC. Find B.
Round angle measures to the nearest degree and
side measures to the nearest tenth.
A. 4.0
B. 24.0
C. 16.9
D. 17.5
1.
2.
3.
4.
A
B
C
D
B. Determine whether the Law of Sines or the Law of
Cosines should be used first to solve ΔABC. Find
mC. Round angle measures to the nearest degree
and side measures to the nearest tenth.
A. 51.3
B. 53
C. 35
D. 60
1.
2.
3.
4.
A
B
C
D
Use the Law of Cosines
AIRCRAFT From the diagram
of the plane shown,
determine the approximate
exterior perimeter of each
wing. Round to the nearest
tenth meter.
Use the Law of Cosines
Use the Law of Sines to find KJ.
Law of Sines
Cross products
Divide each side by sin
Simplify.
.
Use the Law of Cosines
Use the Law of Sines to find
Law of Sines
Cross products
Solve for HKI.
HKI ≈ 25.0°
Use the Law of Cosines
Use the Angle Sum Theorem to find
Angle Sum Theorem
25 + mHIK + 110 ≈ 180
Subtract 135 from each
side.
Use the Law of Cosines
Use the Law of Sines to find HK.
Law of Sines
Cross products
Divide each side by sin
Use a calculator.
Use the Law of Cosines
The perimeter of the wing is equal to
Answer: The perimeter is about 15.1 + 9 + 20 + 16.9 or
about 61 meters.