Law of Sines (AAS or ASA)
Find p. Round to the nearest tenth.
We are given measures of two angles and a
nonincluded side, so use the Law of Sines to write a
proportion.
Law of Sines (AAS or ASA)
Law of Sines
Cross Products Property
Divide each side by sin
Use a calculator.
Answer: p ≈ 4.8
Find c to the nearest tenth.
A. 4.6
B. 29.9
C. 7.8
D. 8.5
A.
B.
C.
D.
A
B
C
D
Law of Sines (SSA)
Find x. Round to the nearest degree.
Law of Sines (SSA)
Law of Sines
mB = 50, b = 10, a = 11
Cross Products Property
Divide each side by 10.
Use the inverse sine ratio.
Use a calculator.
Answer: x ≈ 57.4
Find x. Round to the nearest degree.
A. 39
B. 43
C. 46
D. 49
A.
B.
C.
D.
A
B
C
D
Law of Cosines (SAS)
Find x. Round to the nearest tenth.
Use the Law of Cosines since the measures of two
sides and the included angle are known.
Law of Cosines (SAS)
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
Law of Cosines (SSS)
Find mL. Round to the nearest degree.
Law of Cosines
Simplify.
Law of Cosines (SSS)
Subtract 754 from each side.
Divide each side by –270.
Solve for L.
Use a calculator.
Answer: mL ≈ 49
Find mP. Round to the nearest degree.
A. 44°
B. 51°
C. 56°
D. 69°
A.
B.
C.
D.
A
B
C
D
Indirect Measurement
AIRCRAFT From the diagram
of the plane shown,
determine the approximate
width of each wing. Round to
the nearest tenth meter.
Indirect Measurement
Use the Law of Sines to find KJ.
Law of Sines
Cross products
Indirect Measurement
Divide each side by sin
.
Simplify.
Answer: The width of each wing is about 16.9 meters.
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. Round to the
nearest tenth.
A. 93.5 in.
B. 103.5 in.
C. 96.7 in.
D. 88.8 in.
A.
B.
C.
D.
A
B
C
D
Solve a Triangle
Solve triangle PQR. Round to
the nearest degree.
Since the measures of three sides
are given (SSS), use the Law of
Cosines to find mP.
p2 = r2 + q2 – 2pq cos P
Law of Cosines
82 = 92 + 72 – 2(9)(7) cos P
p = 8, r = 9, and q = 7
Solve a Triangle
64 = 130 – 126 cos P
–66 = –126 cos P
Simplify.
Subtract 130 from
each side.
Divide each side
by –126.
Use the inverse
cosine ratio.
Use a calculator.
Solve a Triangle
Use the Law of Sines to find mQ.
Law of Sines
mP ≈ 58, p = 8,
q = 7.
Multiply each side
by 7.
Use the inverse
sine ratio.
Use a calculator.
Solve a Triangle
By the Triangle Angle Sum Theorem,
mR ≈ 180 – (58 + 48) or 74.
Answer: Therefore, mP ≈ 58; mQ ≈ 48 and
mR ≈ 74.
Solve ΔRST. Round to the nearest degree.
A. mR = 82, mS = 58,
mT = 40
B. mR = 58, mS = 82,
mT = 40
C. mR = 82, mS = 40,
mT = 58
D. mR = 40, mS = 58,
mT = 82
A.
B.
C.
D.
A
B
C
D